Not if they specialize in items that are not well suited to mail order. The urban corner grocery doesn't compete on price with the supermarket 10 blocks away. Locality is the foundation of their business.
I'm not saying that there are enough categories of items that are not well suited for mail order, and have a high degree of value based locality. But this is the central question for such a product.
Retailers whose businesses are protected by locality won't be as reluctant as you imagine. Note that these will be the only successful local retailers over time anyway.
You make a good point, not 100% of the brick and mortar stores would be actively hostile. That wasn't what I meant to imply although perhaps there are more stores, with a high degree of value based locality, than I was originally supposing.
These are also precisely the businesses that currently have the loosest idea of their actual inventory and would incur the most changes to move to the kind of inventory tracking necessary for this to work.
They are also frequently the categories of items that consumers would comparison shop the least. Few people care about going to a few corner groceries to get the right brand of milk. They all carry mostly the same group of products and anything were consumers care about choice (coke/pepsi) they already carry all the options for the same price as everyone else.
The biggest problem, as the parent said, is that brick and mortar stores would be actively hostile to this idea.