If the Night's Watch was supposed to last thousands of years, and was given land, why not have them raise families in the Gift and send all adult males to guard the wall on a rotation?
Because love is the death of duty.
If they have families, they will lose the focus on the defense of the human realms against the Others. And when the time comes when they must choose, they will always choose their families rather than the realm. That is why they give up everything, to be completely focused on one duty.
Maester Aemon explained that part of the vow in detail in his conversation with Jon when it was suspected that Jon would desert for love of his family:
“Jon, did you ever wonder why the men of the Night’s Watch take no wives and father no children?” Maester Aemon asked.
Jon shrugged. “No.” He scattered more meat. The fingers of his left hand were slimy with blood, and his right throbbed from the weight of the bucket.
“So they will not love,” the old man answered, “for love is the bane of honor, the death of duty.”
That did not sound right to Jon, yet he said nothing. The maester was a hundred years old, and a high officer of the Night’s Watch; it was not his place to contradict him.
The old man seemed to sense his doubts. “Tell me, Jon, if the day should ever come when your lord father must needs choose between honor on the one hand and those he loves on the other, what would he do?"
Jon hesitated. He wanted to say that Lord Eddard would never dishonor himself, not even for love, yet inside a small sly voice whispered, He fathered a bastard, where was the honor in that? And your mother, what of his duty to her, he will not even say her name.
“He would do whatever was right,” he said... ringingly, to make up for his hesitation. “No matter what.”
“Then Lord Eddard is a man in ten thousand. Most of us are not so strong. What is honor compared to a woman’s love? What is duty against the feel of a newborn son in your arms... or the memory of a brother’s smile? Wind and words. Wind and words. We are only human, and the gods have fashioned us for love. That is our great glory, and our great tragedy.
The men who formed the Night’s Watch knew that only their courage shielded the realm from the darkness to the north. They knew they must have no divided loyalties to weaken their resolve. So they vowed they would have no wives nor children. Yet brothers they had, and sisters. Mothers who gave them birth, fathers who gave them names. They came from a hundred quarrelsome kingdoms, and they knew times may change, but men do not. So they pledged as well that the Night’s Watch would take no part in the battles of the realms it guarded.
“They kept their pledge. When Aegon slew Black Harren and claimed his kingdom, Harren’s brother was Lord Commander on the Wall, with ten thousand swords to hand. He did not march. In the days when the Seven Kingdoms were seven kingdoms, not a generation passed that three or four of them were not at war. The Watch took no part. When the Andals crossed the narrow sea and swept away the kingdoms of the First Men, the sons of the fallen kings held true to their vows and remained at their posts. So it has always been, for years beyond counting. Such is the price of honor.
A craven can be as brave as any man, when there is nothing to fear. And we all do our duty, when there is no cost to it. How easy it seems then, to walk the path of honor. Yet soon or late in every man’s life comes a day when it is not easy, a day when he must choose.”
AGOT - Jon VIII
This is a great passage which really explains the two most troubling vows of the Black Brothers. First, the vow of celibacy. Second, the vow of neutrality. They must remain celibate for if they have wives and children, their loyalties shall be divided between safety of their loved ones or safety of the realm. And then neutrality because once again, the Black Brothers must not feel any divided loyalties between defense of their former homes and families and defense of the realm.
Until the day of choosing comes, every man is brave and honourable, every man keeps his vows. But that one day comes, as surely as the day he was born, when he must choose. Would he choose his sons? The love of his life? Or the people of the realm? Not every man is strong enough to choose the latter. So they must eliminate the complications to make the vows relatively easier for the Black brothers.
The Gift and the new Gift have in fact been inhabited by normal folks, normal families. And they are occasionally called to defense of the Wall when need be, like Jon called Mole's Town people to Castle Black when Thenns attacked. But they are not Black Brothers. When fight seems hopeless, their first priority will be their families, and they will flee. Just like the Mole Town folks did before Battle of the Wall. Even if we ignore that, if Black Brothers were allowed to own property, start families, the Watch would become eventually a Kingdom in itself, rather than the shield and defenders of all the Kingdoms. And that will sooner or later bring them in political conflict with their neighbouring Kingdoms. Even as things stand, many mad Lord commanders tried to make the watch hereditary, imagine what would happen if there were Houses, families and clans on the Wall as well. They must stand united, all the men of the seven Kingdoms, in defense of all the Kingdoms while staying out of their internal politics.
Jon experienced the truth of Maester Aemon's words despite harbouring doubts initially. When he fell in love with Ygritte, his duty started becoming harder and harder for him. But when the day of choosing came for him at Queenscrown, Jon chose duty and abandoned Ygritte, as much as it hurt him or haunts him still. And yet he failed in some ways again, when he spotted Ygritte while defending Castle Black, his hands won't release the arrow and thus he let Ygritte slip by, simply because he loved her. Who knows how many brothers of Night's Watch Ygritte killed before someone else shot her down?
They weren't. They were required to "take no wives and father no children". Even before contraceptives, there are ways of having sex which have no possibility of pregnancy, and that doesn't even count homosexual encounters.
While celibacy is a way to ensure that, it isn't necessary. It was shown in the novels and books that the members routinely visited brothels, and that this was tolerated, if only unofficially. Maester Aemon made the comment that
If we beheaded every ranger who lay with a girl, the Wall would be manned by headless men.
From a practical standpoint, despite Aemon's poetic explanation, there's also a more practical one; children mean heirs, family, interconnections with other families in the Watch and with people from the South. And at some point, humans being humans, you'll have the equivalent of one or more Houses arising among the Night Watch, and then once that happens, what's the impetus for them to remain neutral in the politics in the South? Having connections means there's a reason to interfering with what's happening down South. If you're Lord Commander of the Watch and your daughter is married to a Mormont and the Mormonts are getting grief from the Boltons, wouldn't you be tempted to flex some muscle to sort that lot out, even just as a threat?
Without children, there's no inheritance. There's none of those interconnections.
Because it generates a conflict of interest that the Watch would rather not have present.
Maester Aemon: Did you ever wonder why the men of the Night's Watch take no wives and father no children? So they will not love. Love is the death of duty."
Game of Thrones - S01E09: Baelor
You may think that having something to defend would make them better at their jobs, but think about this: What about the sons born who'd rather go south? Should they be bound to the wall for the sins of their fathers? If not, then suddenly you have a bunch of Night's Watch who are faced with the same decision that caused Jon to run away for a night. This problem is mitigated by just not letting them form families.
IDK if it's ever mentioned in canon, but this requirement also makes it impossible for the Night's Watch to turn into a dynasty / House, if the Lord Commander had children to pass things on to.
That could easily result in its goals shifting, and the Night's Watch becoming involved in politics. And/or other regions not wanting to send their people.
But when the next generation of Night Watchmen come from all over the land, strangers sent to do their duty, it's more plausible for the institution to survive unchanged for many generations.
Case 1: After Night King's death Two kinds of people to join the night's watch or take the castle black. The first are the found guilty of crimes and join the night's watch for their life. Second, are who join castle black on their own. If you remember in the episode "The Iron Throne" (S08E06) Tyrion told Jon "The world will always need a home for bastards and broken men." The lives of Basterds and broken men in the Westeros is not much fun they are mocked by all. Castle Black and other castles on the wall gives a home to all of them. Also, thieves, looters, rapers etc. are sentenced to die in the Westeros and they are given a choice to restart their lives by taking the castle black. Moreover, the reason for not marrying or father sons is not mentioned in the series but one reason for this could be that thieves, looters and rapers are guilty of crimes so if they father a child or take wives, they will produce a child with same nature. Similarly, for the bastard, offsprings will not have the name of an old house and for broken, they won't be able to raise children as effectively.
Case 2: Before the Night King Apart from the reason for case 1, as maester Aemon said love is the death of duty. So, they were not allowed to take wives or father any child as this might distract them to perform their duty to watch the wall against the night king and the wildlings.
I don't think that part of the oath is just about love and duty, despite the great words from the maester. After all, the men still have families and people they love. Mothers, fathers, brothers, sisters, cousins, etc. Jon himself desperately want to help his brother Robb, probably as much as he would want to help a wife and kids.
The part about not taking a wife has a more practical purpose. A Night Watchman lives at the wall permanently. That means wives and kids would either live with them in the castle, or nearby in some village. It is the same as living in on-base housing for today's military. Wives and kids have to be provided food, health care, education, etc., not to mention security. It's a financial and logistical burden that the NW cannot afford, so it makes a lot of sense to forbid it.