The enterprise c did have a battle bridge that they used mostly for saucer separations, but there were times when they used it saucer in place and there are some ships which have more protected configurations.

Disregarding the IRL reasons of that’s just where it always goes, I believe the in universe reason is that starfleet at its core does not like to identify as a true military organization. It’s why the enterprise C is built like a cruise ship and why despite being a swift science vessel voyager is also very spacious and sleek and elegant on the inside. They do make plenty of starships that are top in class and capable of holding their own against anything else out there, but starfleet is not in the business of making warships. They overtly mention this in DS9 when it is mentioned that the Defiant is officially an “escort vessel” even though it is a very no frills combat vessel.

Of course they can get away with this concession because generally the shields do most of the work when it comes to absorbing hits anyway. Once shields are down if another vessel wants to go for the kill it wont take long for it to tear through the hull. In theory the centralized location also means that the bridge can get additional protection by tilting the saucer away from the enemy(sorry lower decks).

THEY DO HAVE THEM! Every once in a while a trek will show seatbelts and then proceed to forget about them later.

When you consider that the bridge is on the top and center of the saucer section and a very enticing target the constant explosions make a bit of sense. It’s not that the enterprise got shot in the ass and it sent a current up to the computer that monitors shift rotations, no the high powered energy weaponry is aimed right on the other side of the wall. Structural integrity fields, shields, ablative armor, and other technobabble keep the the whole bridge from popping like a balloon when something bad happens.

It’s like if your tv is plugged into a house with breakers and safely on a surge protector it’s not going to keep your tv from getting fried if zeus decides to target that outlet specifically and strike it.