Everyone is bringing up ads or lock-in, but there's another reason companies (beyond Amazon) are going to be squeamish about allowing AI agents to make purchases:

The return rate for AI-purchased products is probably much higher than when a human reviews the page and makes the decision. There are going to be a lot of returns ranging from "I didn't mean to order this" to "It's not what I thought I ordered" because someone asked their agent to do something and an box showed up at their door 3 days later with something they would not have purchased if they were driving the browser.