The Galaxy class starship was designed with the ability to separate the saucer from the stardrive section, so that the “floating city” part of the ship could be left somewhere safe while the rest of the ship galavants off to do something risky. We see this happen precisely once, in the season one episode Arsenal of Freedom. We also see saucer separation deployed for a handful of tactical and or emergency uses (such as against the Borg in The Best of Both Worlds, or to escape the breaching warp core in Generations).
So, this seems like a useful ability to have, and the Enterprise is constantly being sent into dangerous situations. Why not use this ability more frequently?
I think that it ultimately just wasn’t very useful. From a production standpoint, it was an expensive and slow sequence that could be easily avoided without any issues.
From an in-universe standpoint, it was probably a dead-end technology. There are engines, shuttle bays, weapons, and computers that are concentrated in the saucer, which could all be useful in a battle, or in the aftermath of one. The saucer itself doesn’t have any warp engines (they are shown to be able to run on fusion power, so a warp core isn’t a necessity, although it’s a bit slower than antimatter), deflectors, or other FTL mechanism, so if the stardrive is destroyed, it would be effectively stranded, and could be left a sitting duck for anyone who felt like retracing the ship’s steps to hunt down the people trapped on there.
It also doesn’t help that for the most part, it’s rare that a ship will knowingly head into danger, and have the opportunity to drop off its stardrive section. Danger usually happens to the ship on the spot, at which point, it would be too late to go and drop off the saucer section.
The Prometheus project might have been an attempt at salvaging the concept, replacing the saucer with a whole starship, but given that it wasn’t used in later ships, it was likely deemed a failure, possibly because at that point, you’re just building multiple starships, and might as well make them fully fledged craft on their own.