"it makes no sense" isn't really an argument one way or the other, since I could say the same about the 10 second count to begin with, or the 35 second clock, or the fact that the offense starts shooting free throws after 7 fouls in a half.
The 10 second count forces the offense to bring the ball up relatively quickly (to speed the game up), and implicitly to reward the defense for playing full court. That is its purpose. It resets because someone decided that it would give the defense too much of an advantage to not have it reset. There's no danger in sabotaging the speed of the game by resetting the 10 second count, because you still have the shot clock (which doesn't reset, as noted) as a sort of safety net to keep things moving. It's purely a question of balance and fairness, not "sense".
I'd be very hesitant to change that rule -- and in general any rule, without careful consideration. It's one of those rules that benefits teams with less physical talent. Or, put another way, skewing it in the favor of defense hurts mid-majors, which hurts the reason most people tune into March Madness (upsets).
Don't try to hurt the game just so your favorite team can force more turnovers.
