As a user I want the agent to be my full proxy. As a website operator I don’t want a mob of bots draining my resources.
Perhaps a good analogy is Mint and the bank account scraping they had to do in the 2010s, because no bank offered APIs with scoped permissions. Lots of customers complained, and after Plaid made it big business, eventually they relented and built the scalable solution.
The technical solution here is probably some combination of offering MCP endpoints for your actions, and some direct blob store access for static content. (Maybe even figuring out how to bill content loading to the consumer so agents foot the bill.)