In The Return of the King, Gandalf is talking to Pippin and says,
If the river is taken... if the garrison at Osgiliath falls, the last defense of this city will be gone.
But after Osgiliath falls, Minas Tirith mounts a very effective defense complete with a nearly unbreakable gate, catapults, soldiers, etc. Gandalf even tells the soldiers to stand their ground when Denethor tells everyone to flee.
What did Gandalf mean by this?
A wide river is a significant barrier to the movement of troops as they must cross the river by ford, bridge or boat, which slows them down and makes them vulnerable to attack.
There are places where such crossings are easier than others, and these are the places where bridges and cities are built. That must explain why Osgiliath was founded here, and we know that there was a stone bridge over the river at this point (until it was destroyed). I think we can assume that Osgliath is a good place to cross when attacking Minas Tirith.
Denethor explains why he believes it is where the crossing will be made:
‘Yet,’ said Denethor, ‘we should not lightly abandon the outer defences, the Rammas made with so great a labour. And the Enemy must pay dearly for the crossing of the River. That he cannot do, in force to assail the City, either north of Cair Andros because of the marshes, or southwards towards Lebennin because of the breadth of the River, that needs many boats. It is at Osgiliath that he will put his weight, as before when Boromir denied him the passage.’
The Lord of the Rings Book Five, Chapter 4: The Siege of Gondor
Page 816 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)
Denethor's judgement was impaired by Sauron's influence, but he understood strategy. I think we can believe his assessment that crossing at Osgiliath was the most advantageous place for Sauron's forces.
I should acknowledge that the maps show the river bends west as it goes south of Minas Tirith and is much closer to the city at the Harlond (south-east of the gates) than it is at Osgiliath. I think we must assume that there are reasons (perhaps the width of the river) that make this a difficult crossing point for an enemy force.
While the defenders put up what you say is "a very effective defense" it really isn't all that good. A city made of stone built into a mountain with only 1 way in or out has no way to feed itself. The defenders are pushed off of the wall, and the lower levels are taken, don't remember exactly but I believe they are in the 3rd ring when the Rohirrim arrive. They are less defending the city and more trying to live as long as they could. Had Rohan not arrived, they would have been killed to a man. However, if they had held the river, and were fighting there instead of in their streets, the people could have been evacuated, and food could have been brought in for a long siege, and reinforcements could arrive and have somewhere to stage.
Think about WW2 for a minute, the Allies staged in England to mount their invasion of Europe. Think of England as Osgiliath, really close to the enemy and constantly under threat of attack. Had England fallen, the Allies would not have had anywhere to stage for their invasion, and WW2 might have ended differently.
The defense was also not really that effective. Standard military practice back in the day was to besiege the city, cause them to surrender or starve, not outright attack such impressive fortifications as Minas Tirith had, yet they lost their strongest defenses in less than a day. The gate was breached, the wall was taken, and the soldiers were dying en masse. All before dawn the next day. That doesn't sound very effective to me.
