They currently collect sales tax in 24 states[1,2], and I'm guessing the writing is on the wall in the other 26. I don't know if there's any truth to this Radio Shack rumor, but I'd expect that avoiding tax nexus status probably isn't as big a deal for them as it used to be, because they're going to be forced to do soon, one way or another.
It might, but Amazon has been slowly losing the sales tax fight [1]. I imagine they'll do this in phases or do it in places where they're likely to have sales tax levied on them in any case.
For Amazon, getting faster and more convenient delivery might be worth the cost. It helps them in their fight against brick and mortar retailers, and if they're careful about it they could probably leverage a limited physical presence pretty well.