In a world where "inertial dampeners" exist and making invisible forcefields is pedestrian, physical seatbelts aren't terribly important. If inertial dampeners outright fail in a spacecraft designed for them you can expect to be reduced to a souplike homogenate whether you're wearing a seatbelt or not.
People get tossed out of their seats every other episode in star trek. I'm sure I've seen multiple "medical team to the bridge"s due to someone getting knocked loose by the ship shaking and hitting their head on a console.
That and in the future we'll apparently forget everything we ever learned about electrical codes and the proper way to build things so they don't spark and catch fire at the slightest provocation.
I actually saw a reasonable explanation for this once: battleshort[1].
That is, sometimes equipment has its fuses bypassed because under battle conditions it is better to have the equipment working in a dangerous state, than not working at all.
So when the ship goes to red alert all the major systems are automatically put in battleshort mode. So a couple of ensigns die rather then the weapons stop working because a fuse blew.
Also, Star Trek uses a plasma grid to distribute energy, not simple electrical lines. I think I remember reading somewhere (this may have been fan theory) the sparks flying off are a pressure-release so it doesn't just straight explode.
That is a very old-school approach so. But it could be an in-uniberse explanation. Overall so, Federation, and Star Trek equipment in general, just seems so incredibly unsafe. Very easy to jury-rigg repairs and modify it so, especially the shield generators!
Course, given the accelerations in Star Trek you are red smudge without them anyway. But then there is all the flowing around around the bridge, engineering, everytime a ship is hit... Maybe a seatbelt wouod have helped!
Or some space space suits, proper footware for away missions. Alongside clothing...
Starfleet is the Federation's solution to the existence of type-A personalities, giving them something exciting and challenging to do in order to prevent them from screwing up the socialist utopia for everyone else. All Starfleet technology is optimized not for efficiency, but for excitement; giving Starfleet personnel brushes with danger, interesting puzzles to solve, and opportunities to improvise and collaborate. Wouldn't surprise me if the inertial dampeners on the bridge are specifically tuned to toss people around a bit during battles to make them more immersive and raise the stakes. Why else would computer terminals spontaneously explode when the shields take a hit?
