That's irrelevant from Amazon's perspective. If an agent is popular enough and has some fingerprint they can identify, they have a strong incentive to block it.
Agents that scrape and digest web data are entirely anathema to brand-reliant and advertising-reliant vendors and marketplaces. Even human assistants could be trusted to develop brand attachment and respond to advertising meant to shape their preferences. And while LLM agents are still manipulable, that's a frontier that nobody really knows how to navigate effectively yet, at least not to the degree of optimization modern vendors and marketplaces (especially Amazon) have acheived.
It's quaint to imagine what AI agents might do for consumers in the naive internet that preceded their emergence (if you ignore their vulnerabilities and flaws), but that's not what they'll be able to achieve as that same internet responds to them -- at least not at Meta scale. It's not very different than how social media companies once offered, and then aggressively withdrew and policed, API's to their graphs and feeds. Those open API's simply aren't compatible with the business objectives that keep these companies running, no matter what cool and profoundly user-friendly things could be built on them.
The same kind of incompatibility applies to AI agents when it comes to e-commerce. It won't be a permitted thing until, and except for where, vendors/marketplaces can assert control over the agents themselves and manipulate them to ends comparable to what they can achieve with human consumer sentiment already.