You can buy a Claude Code subscription for $200 bucks and use way more tokens in Claude Code than if you pay for direct API usage. Anthopic decided you can't take your Auth key for Claude code and use it to hit the API via a different tool. They made that business decision, because they thought it was better for them strategically to do that. They're allowed to make that choice as a business.

Plenty of companies make the same choice about their API, they provide it for a specific purpose but they have good business reasons they want you using the website. Plenty of people write webcrawlers and it's been a cat and mouse game for decades for websites to block them.

This will just be one more step in that cat and mouse game, and if the AI really gets good enough to become a complete intermediary between you and the website? The website will just shutdown. We saw it happen before with the open web. These websites aren't here for some heroic purpose, if you screw their business model they will just go out of business. You won't be able to use their website because it won't exist and the website that do exist will either (a) be made by the same guys writing your agent, and (b) be highly highly optimized to get your agent to screw you.