A bow will easily kill any animal. Personally I think a bow will kill any animal just as fast as a gun shot to the vitals. Actually even faster. Even a youth weight bow such as 45 pound draw weight will easily pass through deer and even black bear. An arrow is so deadly that any animal shot through both lungs or the heart will collapse most of the time under 10 second. 6 seconds is more realistic. And they will usually be dead within 30 seconds.

A compound is the most powerful for it's draw weight but traditional bows are just as deadly and a 45 pound draw weight long bow even though it shoots a little slower will still kill deer sized game just as quickly.

If they would prefer to set minimum draw weights for the larger game, I suggest something around:
50 pound for compounds
55 pound for recurves
60 pound for longbows.

These figures show bow weights which should easily put down any large game.
For smaller game like deer, 35 pound will do the job but maybe 40 pound should be the minimum for compounds.

Show them some american hunting videos of moose and bear and elk being taken with bow and arrow.