Companies don't want it to be easy to cross shop their competition, the whole premise of Amazon is that it's so easy and simple you don't even check the competition. AI agents are leveling the playing field and helping customers find the best deals, so of course they're being banned
Agents are likely the slow death of Amazon. Muse could decide to sell anything and group buy their way into the everything store.
It's really hard to build a walled garden just for human users, and not for agents. Have to pick a side.
It's mostly because of ads though. Not cross shopping.
Current AI agents overindex on price. The price has to be reasonable but I often rank fast shipping and easy returns higher than price.