I don't think it does make sense. I think Amazon is way overestimating brand loyalty, and underestimating how much of their success comes from being a one-stop shop for everything.

I'm using Claude for everything from finances to dinner planning to project planning. If Amazon doesn't let Claude search and buy, I'm not abandoning Claude, I'm abandoning Amazon.

As long as my actions are as simple as possible, I don't care whether Claude is searching 5000 online retailers or only 4999, minus Amazon. I'm certainly not going to say "ok, this project requires buying 13 things for about $500, but I don't see amazon in the list, so let me go manually search for each one on Amazon and see if they might have a better price or something."

This is Walmart / Apple Pay all over again. Yes, near-monopolies, lots of power. But they got there by making things easy for consumers. Making things difficult to force consumer behavior never ends well.