Absolutely, but it is a tricky argument. I'm sure one could kill a bear with a perfectly placed .22 bullet, or an arrow shot from a modestly powered recurve for that matter. But that kind of accuracy is difficult to achieve consistently. Using a more powerful weapon gives you a little leeway and helps ensure humane harvesting.

Using a 40 to 50 lb recurve for bear hunting may be legal in some places but it is not something I would recommend or attempt myself. A good broadhead shot from a modern 60 to 70lb compound bow will likely pass clean through most big game, bear included. This will result in massive bleeding and usually a quick, humane kill. A lightweight recurve does not come close in that department.

A high-end modern 70lb compound can shoot a 500 grain arrow at maybe 275 fps, which gives about 85 ft/lbs of kinetic energy. A 40 lb recurve might be able to shoot a 400 grain arrow at 180 ft/lb, so the kinetic energy is a little under 30 ft/lbs (way less than the 50 ft/lbs minimum often cited for big game - bear, moose, elk).

It's really a massive difference and while I do agree that a heavy modern compound is overkill for most game in our hemisphere it's good to have some extra power just in case.