I know the answer is because it would have been a dick thing to do to say "No get your ass back to sick bay" and so Chekov could payback in kind Khan for all his hospitality.
But really.....This was just another in a line of things in TWOK that shows Kirk really wasn't on top of his game.
1. Lets another Federation ship that is acting strangely, and flat out lies to them about a mechanical issue they're having, approach right next to the Enterprise and doesn't raise his shields, even though the regs say he should and even when Reliant raises hers he still hesitates until it's too late.
2. Seems to forget that Reliant is carrying this weapon capable of destroying everything in sight an that maybe he should either use the nebula to try and slip away for help, or have a commando team ready to beam over immediately after they disable Reliant to secure Genesis on the off chance Khan is still alive and willing to use it and give up his own life to fulfill his vow of revenge against Kirk. Something not too far fetched to think about given how fanatical and rage filled Khan has been throughout and basically shown he'll stop at nothing to get his vengence.
3. Seems to completely not notice his best friend and right hand man slips away with a disaster looming and even after they've escaped doesn't turn to where he should be and say something.
4. During at least for the last 30 seconds of the Genesis countdown, could be more because we don't know when he took up this posture, is just sitting in his chair with his arms folded basically saying "Well, we're fucked this time sorry folks nothing I can do" When, as the commanding officer, he should been screaming in into the intercom at engineering non stop for someone to respond or do something right up to the moment he is blown to atoms by the genesis explosion.
And then there is the Chekov thing. Sure it was nice Chekov came to the bridge to ask if he could help, but he is still clearly F'ed up from the Ceri Eel. He is sewating heavily, walking unsteadily and speaking in a slow and halting manner, all of which indicate he is not fit for action. But instead of ordering him back to sick bay or telling he can just hang out on the bridge he tells him to man the WEAPONS console
Right in the middle of a battle where all computer weapon locking devices are not functioning and you have to aim manually?
I mean really Chekov's that important that even though his equalibrium and balance and motor skills are still impaired you're going to let him be the one to shoot at the Reliant. I mean couldn't Sulu do it? He fired all the phaser shots so far and in STIII Scotty was able to fire photon torpedos from the forward station, so it wasn't a matter of they specifically needed someone at the console Chekov was assigned to. Really as a commanding officer isn't it your duty do decide "Uh...you still look pretty messed up, just grab a seat and hang out" and not give such an important task to someone like that just because you like him.
Well of course Kirk's faith was proved correct as both torpedoes Chekov fired (I'm assuming sulu still fired the phasers) hit and caused catastrophic damage....but really was it a wise command decision? I mean if you play a game of Russian roulette with 5 others and win...OK you were lucky and won. Great, but was it smart to play the game in the first place?
Just seems Kirk couldn't see the bigger picture in many instances here.
But really.....This was just another in a line of things in TWOK that shows Kirk really wasn't on top of his game.
1. Lets another Federation ship that is acting strangely, and flat out lies to them about a mechanical issue they're having, approach right next to the Enterprise and doesn't raise his shields, even though the regs say he should and even when Reliant raises hers he still hesitates until it's too late.
2. Seems to forget that Reliant is carrying this weapon capable of destroying everything in sight an that maybe he should either use the nebula to try and slip away for help, or have a commando team ready to beam over immediately after they disable Reliant to secure Genesis on the off chance Khan is still alive and willing to use it and give up his own life to fulfill his vow of revenge against Kirk. Something not too far fetched to think about given how fanatical and rage filled Khan has been throughout and basically shown he'll stop at nothing to get his vengence.
3. Seems to completely not notice his best friend and right hand man slips away with a disaster looming and even after they've escaped doesn't turn to where he should be and say something.
4. During at least for the last 30 seconds of the Genesis countdown, could be more because we don't know when he took up this posture, is just sitting in his chair with his arms folded basically saying "Well, we're fucked this time sorry folks nothing I can do" When, as the commanding officer, he should been screaming in into the intercom at engineering non stop for someone to respond or do something right up to the moment he is blown to atoms by the genesis explosion.
And then there is the Chekov thing. Sure it was nice Chekov came to the bridge to ask if he could help, but he is still clearly F'ed up from the Ceri Eel. He is sewating heavily, walking unsteadily and speaking in a slow and halting manner, all of which indicate he is not fit for action. But instead of ordering him back to sick bay or telling he can just hang out on the bridge he tells him to man the WEAPONS console

I mean really Chekov's that important that even though his equalibrium and balance and motor skills are still impaired you're going to let him be the one to shoot at the Reliant. I mean couldn't Sulu do it? He fired all the phaser shots so far and in STIII Scotty was able to fire photon torpedos from the forward station, so it wasn't a matter of they specifically needed someone at the console Chekov was assigned to. Really as a commanding officer isn't it your duty do decide "Uh...you still look pretty messed up, just grab a seat and hang out" and not give such an important task to someone like that just because you like him.
Well of course Kirk's faith was proved correct as both torpedoes Chekov fired (I'm assuming sulu still fired the phasers) hit and caused catastrophic damage....but really was it a wise command decision? I mean if you play a game of Russian roulette with 5 others and win...OK you were lucky and won. Great, but was it smart to play the game in the first place?
Just seems Kirk couldn't see the bigger picture in many instances here.