If that’s the way it went with indian dogs, you can bet you a$$ those dogs weren’t much good for anything. Their breeding wasn’t selected for any useful skill and likely there wasn’t any selective breeding at all. Probably about like trying to train a husky to fetch, only worse. No wonder the european breeds displaced them.
Naw, they don't fetch do they! But they can beg for giant pretzles.
The Indian dogs like those Carolina wild dogs pretty much live in wetlands or swamps. Best thing they can do is hang around your house and watch your stuff at night. Not a house dog!
The horse displaced them. Indians used dogs as beasts of burden, pulling travois with belongings, shelter material, etc, before the arrival [re-arrival, actually], of the horse with the Spanish. After that, dogs were kept mainly as watchdogs for the camp.