They work, but they don't seem to be shielded to protect them from phaser fire -- a big flaw when you think about it.
Not against asteroids, which very rarely fire back, I guess.
Kirk seemed to think that shooting down Starfleet torpedoes with phasers was a viable technique in ST2:TWoK, though - it simply was "too late", as Sulu put it. Perhaps photorps are harder to kill than Nero's torps, perhaps not. But apparently it's not worth the hassle to equip late 23rd or 24th century ships with anti-torpedo phasers; diverting that power to shields is the tactically preferred option.
for all they know, they can't shoot them down
Would they assume they can't, when the Enterprise
and the Kelvin
We can of course assume they can't shoot, period - perhaps most of those ships had too few and too poorly trained crew to actually be combat-capable?
Enterprise figured it out (it's technically easier to shoot down something coming at you than it is crossing your path too).
Except Sulu shot down targets that were crossing his path. And that's actually easier, because things coming straight at you can easily maneuver erratically from side to side, creating high angular velocities, whereas things flying past you create less erratic paths with lower angular velocities with the same maneuvers. Plus there's less terror involved...
I doubt they could have killed Narada though via conventional means. Even with Vengeance. Kelvin warping into her didn't, and that's a lot of energy.
didn't go FTL from what we observed. But yeah, the sheer bulk of the target seems to protect it from most things.
Then again, the impact of the Kelvin
rendered the Narada
incapable of firing at the shuttles, or pursuing them. Basically, then, if a single cadet ship rammed the mining rig, the rest could spend the following two days firing at the rig with impunity! Surely that would give some results.