Have you ever tried gathering 2,000 calories every day for a week?
Hunting is more work but the caloric payoff is orders of magnitude greater.
It is all situational. If there is plenty of plant calories around to be gathered, you can bet there will be plenty of herbivore and omnivore competition for those plant calories.
If there is plenty of game, easily hunted, hunting can be far more productive than gathering.
It appears to me, the Americas offered plenty of game and easy hunting for the first thousand years or so. Then the continents were full of hunting tribes, the easy big game was hunted to extinction, and life became much harder.
I had a girl tell me that the women gatherers of a tribe supplied most of the food.
My response is “How much would they gather if the male hunting parties were not continually patrolling the tribe’s territory and keeping out neighboring tribes from encroaching?”