Part of the genius of Amazon Prime is that it capitalizes on the sunk cost fallacy. I (happily) give them $100/yr to allow me to shop there with no shipping costs, and, by god, I'm going to get my money's worth. I'm not going to squander my sunk costs by shopping at some brick-and-mortar store! IMO, this is one of the biggest hurdles Walmart has to overcome.
I think Walmart is right that accessibility and immediacy is sometimes desirable. If I blow a tire on my bike and I want to ride to work tomorrow, I'm still heading to a brick-and-mortar store. I can grab a few groceries while I'm there.
I do also think they could leverage their distribution network. There's a Walmart on pretty much everybody's way home from work, and it's only a minor inconvenience to stop in to pick something up. I've done it before for larger items that Amazon wouldn't ship free.
But that Prime, though! I love it, and I wouldn't give it up, and there's no way I'd pay somebody else for a similar service in addition to it. That's where they've really got me. That's how Amazon went from something I only used for hard-to-find items to my go-to vendor for practically everything.