At the same time, the gravity systems are designed by the best engineers in the Federation because they never, ever, give out, even when the rest of the ship is disintegrating.

The explanation I've always had- I think this was from some official source but I could have just made it up.

Starfleet ships use EPS (Electro-Plasma System) to route power around the ship in the form of electro-plasma (a highly energized form of plasma). The warp core generates a lot of this plasma, which is piped through conduits to various devices around the ship. The EPS system and its related systems generate a lot of treknobabble about 'scrubbing plasma conduits' (apparently done from the outside using a field generator tool, but still boring), 'replacing plasma relays' (the valves that route plasma around, apparently they go bad frequently); problems like ruptured plasma conduits are dangerous and require immediate repair, etc.

Because this all works in a grid system, whenever the ship takes damage (especially energetic damage like weapons fire) the EPS conduits can carry energy spikes all over the ship. That's why as the ship takes damage you see random small explosions and sparks all over the place- something hits or spikes the EPS grid and the shockwave ends up, well, wherever in the grid it ends up.

Of course many EPS conduits go to bridge terminals, especially as those terminals may have direct connections to the ship systems in question.

Of course in reality this would be seen as a horrible safety risk, and a bridge terminal that could probably run on a car battery shouldn't have explosive plasma running through it especially when it can explode and harm the operator. In fact one could argue a safe starship should keep all EPS stuff as far away from any essential human-inhabited areas of the ship as possible (especially the bridge).

One counter to that might be that perhaps the consoles actually play some role in EPS switching, but that seems a bad tradeoff to me.

When a console overloads, it’s way better to be thrown from the seat than to be burned and electrocuted. The lack of seat belts is a safety feature.

In an episode of DS9 I heard some of the characters mention that they not only have deflector shields, but also "structural reinforcement shields." So whatever science-fictiony force field is used to protect them from phasers and micrometeorites is also coursing through the skeletal structure of the ship.

When I heard this it immediately clicked in my mind: whenever the ship is hit with phaser fire the explosions happening inside are recoil from these internal shields. Perhaps the catastrophic damage prevented by structural reinforcement shields outweighs the localized damage of potentially fatal recoil.

That is my favorite explanation, anyway.

(This assumes all ships have structural reinforcement shields, and not just the Defiant.)

Consoles are rigged with explosives to keep the lower decks in line.

Over at Daystrom, this comes up from time to time. I've formed a head-canon for it as well. To quote one of my comments on a thread there regarding the explosions (and the "rocks"):

My understanding is that the "rocks" are a product of the electroplasma system being exposed to air. Whether that is some sort of coolant that is meant to seal the EPS leak in that console or some sort of EPS byproduct reacting in air, I don't remember or have a head-canon for it.

All of that said, if I form this reply into one worthy of Daystrom, then I say it is an intended safety mechanism to protect the crew against catastrophic failure of the EPS conduits.

So, the consoles are exploding from the failure of the EPS conduits and the expansion of the coolant.

What about the rocks, though? It always seems like a starship is built around a massive quarry.

"Haven't you people ever heard of fuses?!?" -John Crichton