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?
They highlighted the tactical disadvantages in The Best Of Both Worlds. In a battle situation, the saucer section’s phaser banks, impulse drive, and fusion generators are of high importance.
There are also alternatives. In DS9’s episode introducing the Jem’hadar, The Odyssey simply dropped off their families before heading to the Delta quadrant.
I’m the event a hostile force is encountered, it is likely the saucer section would just be pursued and destroyed, as it could only flee on impulse or sustain a low warp is released at warp.
So they really only used it the only times it was practical: facing Q, facing the arsenal of freedom (as the automated system only attacked ships in orbit), and as a life raft after the star drive was destroyed as in Generations.
It might also be noted that prior Enterprises had the ability to separate the saucer on an emergency. It was just never used on screen, and also would probably require a spacedock to reassemble.
I personally think it was just an experiment that didn’t work out. Perhaps they just reverted to emergency separations.