TL;DR - Wildfire is difficult to produce and very volatile.
Wildfire is created by Alchemists Guild which is a secret they posses alone. Their order is no longer prevalent in Westeros and the remaining members seem to be in King's Landing alone. This is the first reason why other houses do not use it.
The substance was the pyromancers' own term for wildfire. They called each other wisdom as well, which Tyrion found almost as annoying as their custom of hinting at the vast secret stores of knowledge that they wanted him to think they possessed. Once theirs had been a powerful guild, but in recent centuries the maesters of the Citadel had supplanted the alchemists almost everywhere. Now only a few of the older order remained, and they no longer even pretended to transmute metals...
...but they could make wildfire.
A Clash of Kings - Tyrion V
The Guild created the Wildfire under the direction of the Targaryen's namely "The Mad King" Aerys II (see the Wildfire Plot) which was then hidden underneath the city.
"There is a vault below this one where we store the older pots. Those from King Aerys's day. It was his fancy to have the jars made in the shapes of fruits. Very perilous fruits indeed, my lord Hand, and, hmmm, riper now than ever, if you take my meaning. We have sealed them with wax and pumped the lower vault full of water, but even so . . . by rights they ought to have been destroyed, but so many of our masters were murdered during the Sack of King's Landing, the few acolytes who remained were unequal to the task. And much of the stock we made for Aerys was lost. Only last year, two hundred jars were discovered in a storeroom beneath the Great Sept of Baelor. No one could recall how they came there, but I'm sure I do not need to tell you that the High Septon was beside himself with terror. I myself saw that they were safely moved. I had a cart filled with sand, and sent our most able acolytes.
A Clash of Kings - Tyrion V
That secret involves spells that only the Alchemist's know and even for them it is difficult:
"We were, my lord Hand, my brothers and I have been laboring day and night from the first, I assure you. It is only, hmmm, we have made so much of the substance that we have become, hmmm, more practiced as it were, and also"—the alchemist shifted uncomfortably—"certain spells, hmmm, ancient secrets of our order, very delicate, very troublesome, but necessary if the substance is to be, hmmm, all it should be..."
A Clash of Kings - Tyrion XI
Cersei initially found these stores and then Tyrion recruited the Guild to make more for Battle of Blackwater.
The pyromancers kept their recipe for wildfire a closely guarded secret, but Tyrion knew that it was a lengthy, dangerous, and time-consuming process. He had assumed the promise of ten thousand jars was a wild boast, like that of the bannerman who vows to marshal ten thousand swords for his lord and shows up on the day of battle with a hundred and two. If they can truly give us ten thousand . . .
He did not know whether he ought to be delighted or terrified. Perhaps a smidge of both. "I trust that your guild brothers are not engaging in any unseemly haste, Wisdom. We do not want ten thousand jars of defective wildfire, nor even one . . . and we most certainly do not want any mishaps."
A Clash of Kings - Tyrion V
The second reason other houses do not use it is (as seen in the above quotes) a, Wildfire is time consuming and dangerous to make and has a shelf life. Once you have some, it may not work as you intend it to either,
An arrow could be aimed, and a spear, even the stone from a catapult, but wildfire had a will of its own. Once loosed, it was beyond the control of mere men.
A Clash of Kings - Tyrion XIII
Jaime also agrees with that assessment
Jaime ignored that. "If these flames spread beyond the tower, you may end up burning down the castle whether you mean to or not. Wildfire is treacherous."
A Feast for Crows - Cersei III
So if a another house wanted it use it, they would first have to hire the Alchemists Guild, which I'm sure during the Targaryen and Lannister reign would not have been taken kindly to. Next the would have to wait quite a long time for large enough store to be effectively used in battle to be made. Finally, they would have to hope and pray they stored and handled it properly without killing themselves.
Wildfire was Tyrion's last ditch effort to protect the city.
