The company I work for actually already tried it like 20 years ago, got immediately scammed with an expensive credit card chargeback (we'd already passed the money on) and the boss pulled the plug on it.

I think most shops don't want you to see competitors prices and be able to swap to them with a click. They were like walled gardens and only begrudgingly use Amazon because some people think the rest of the internet is scary and don't trust it.

Amazon already shows us where that approach goes. It results in a melting pot of the cheapest possible crap.