David said "you can't" to a specific plan of Kirk's. First of all, his character is never established as being omniscient or infallible. Secondly, even if he was correct in saying that X can't be done, that doesn't automatically preclude Y or Z.
But the scene would make no sense if Y or Z were possible. David says "You can't shut it down, the process is inreversible or something". Kirk says "We have to run, then...", but the ship isn't up to it. "Great, we're all gonna die!" is what everybody's body language, faces and even dialogue is constantly expressing from that timepoint on. Now, if David did know of an alternative course of action, it's quite implausible that he
wouldn't butt in with "Hey, wait, what about doing this instead...?" - no matter how harebrained that scheme.
How could beaming it possibly trigger it?
Quite plausible, if the whole device is based on some sort of adaptation of the transporter principle in the first place. Transporters may be able to move delicate objects without harming them, yes. But the use of transporters may still send out types of radiation or subspace resonance or whatnot that will trigger the Genesis device into doing something really, really bad, even before the actual transport process starts.
Indeed, one might argue that David didn't say "You can't (shut it down)", but "You can't (beam over to shut it down)", exactly because transporters would be incompatible with the device.
Really, if there was room for argument in that situation, the argument would have taken place. Perhaps arguments between disciplined Starfleet officers are rare, but David the all-knowing civilian expert wouldn't have been held back by regulations, or by faith in the ability of Starfleet to come up with answers for him.
I already gave the example where he shot and killed the knight on the horse with a revolver, showing that Kirk is willing and able to kill in defense of himself or his crew. Also, I seem to remember Spock and him killing with homemade bows and arrows in one of the episodes. Plus, he's caused enemy deaths by firing on their vessels with his ship's weapons too, which is no different (just less close and personal).
All of those cases have one thing in common: Kirk didn't have a stun weapon available.
When he did, he always used it instead of a lethal one. So carrying both a Colt and a phaser wouldn't be an option he'd lightly choose, because it would mean giving up on one of his (and Starfleet's) principles. A phaser, a tranq gun and a Colt, perhaps (Stargate did that a lot). But not just phaser plus a lethal weapon.
Fire all phasers [..] instead of just one phaser pulse from the primary phasers.
But that's the same thing. Starships in the TNG era (and in TOS, for that matter) always fire only one beam or one pair of beams. So that's apparently the most destructive way to operate the weapons; using multiple beams would be less desirable for some reason, perhaps because that would divide the finite amount of output power between multiple emitters that each waste a fixed percentage of power. Channeling everything through one beam would be better, then.
Say, when Riker is in
really deep shit and not just his ship but the entire UFP is at mortal risk from the Borg in "BoBW", he commands all weapons fired, and what we see is, again, a
single phaser beam plus torpedoes. Now, adding torps to the mix might be a good idea - but we repeatedly hear that torps are not close range weapons, and would probably do just as much harm to the E-D as to the enemy if used in ST:GEN!
Timo Saloniemi