The right way to implement "ship to store" is using something like "amazon locker". Assuming that's the correct route, amazon will win, because it can choose better locations than a walmart store . And in retail location is everything.

But the fact that amazon has tried some lockers but it doesn't seem the common way to buy stuff, and there's no huge scaling effort from amazon, seems to indicate that people prefer to recieve packages at home.

And bezos understands that in this game, if you want to make profits, you need for customers to love using your services.Having that ability at low enough costs could earn you a monopoly. And than might be the time to play with "amazon lockers" and other cost cutting measures.