NY has no caliber restriction at all. The law is "center-fire rifle". As far as I can tell, the cartridge used is almost never the cause of lost and wounded animals. I have seen wounded, unrecovered animals that were shot with about everything, long bows, compound bows, 12ga/20ga/10ga slugs, buckshot, rifles.... about everything.
Far and away, I see two factors that influence wounded/lost animals. The first is bad luck. It be a bump the scope took that we didn't know, might be an animal jumping just as the shot breaks, might be a twig in the way that we didn't couldn't see. The second (far more common) is hunters taking shots that they shouldn't be taking. Too far, too small, wrong angle, rush, running animal, misjudging distance, etc. etc.
I can't think of a single instance wherein the hunter took a good and reasonable shot at an animal in a good shooting position/manner and lost the animal due to insufficient lethality of the chosen weapon. In fact, far as I can tell, those with the weakest weapons (archery) wound fewer deer than those with the most power (shotguns).
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
You do not HAVE a soul. You ARE a soul. You HAVE a body.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.