Actually, the "corner store" doesn't have to collect sales tax. The "corner store" collects sales tax for the jurisdiction it is in. (Car dealers are an exception because of licensing.)
CA says that its residents owe sales tax on anything that they use within the state. For example, if a CA resident walks into a store in Nevada, buys something, and takes said something back to CA, CA thinks that it is owed sales tax.
I've never seen a Nevada store collect CA sales tax for sales to CA residents. I've never even seen someone suggest that said store has an obligation to collect CA sales tax. Why is Amazon different?
And yes, most Nevada stores will ship.