I agree with most of what you're saying. OP asked so I tried to game it out the best I could. Personally I think we need to approach gun legislation like we do cars. License to carry in public, strict rules about thier usage, and automatic max penalties and enhanced charges for any crime committed while carrying a gun (legally or otherwise), which can include losing your carry license.
I would say though that your trainer wouldn't be thwarted by a bullet ownership limit either, it would just slow down their training. They'd buy their 50, shoot them, then have to buy more all of which could be done at the range.
I broadly agree with you about lists, eventually they will be misused. But the chilling effort would be the point. A chilling effect isn't universally a bad thing, modern HR practices had a chilling effect on sexual harassment in the workplace, banning nazi symbols had a chilling effect on the spread of fascist ideals in post war germany, etc. In this case the chilling effect of reducing the amount of ammo purchased might be beneficial.