Provided that Starfleet did have Kirk under constant, strict surveillance and worry about him snapping a twig, why test the M5 on his ship? Why not test it on a ship where the captain wouldn't be as unhappy with becoming redundant?
As for Wesley having more faith in the M5 than Kirk, that doesn't say anything about Kirk. Wesley likely had been a starship commander before so he is obviously aware that computers can and do malfunction. Sure, people snap twigs too, but what's more likely; Kirk snapping a twig all of a sudden or a brand spanking new, never been tested in live conditions computer malfunctioning? The fact that he's believed all this nonsense about how wonderful the M5 is proves he's a freakin' loon. Sure, it's been hyped up, but never tested in live conditions and Wesley retains absolutely no skepticism. Heck, Scotty knew plugging that thing in the Enterprise was a bad idea and he was just going off what the M5 was *supposed* to do.
And people keep mentioning the off switch. Those can malfunction too. Wesley is lacking in the critical thinking skills department. He's not considering more than one possibility. That's the point.