Fair point, but it depends on where you live. Many places have lots of smaller animals like squirrels and rabbits. Even some deserts have rabbits and field mice, etc.
But, those animals are trained to stay away from humans. You won't see them out in the wilderness, at least not for long. And, you won't be able to catch up to one in the brushes where there's thorns, bushes, and all kinds of stuff that can stick you.
You won’t see them while you’re hiking, because you’re making lots of noise and likely not out at the right times. Hunting , especially primitive hunting, is usually either lots of traps and snares or lots and lots of waiting.