Would agents use a website's own semantic search endpoint?

When an agent needs an answer from a website, it often searches, fetches one or more pages, strips the HTML, and guesses which page is authoritative. I've been prototyping a different approach in a small open-source package called Agentize. The site owner chooses the public content, builds a semantic index locally, and exposes search plus Markdown resources under /agents/*. Results keep canonical URLs so an agent can still inspect the source. I built the package, so I have a stake in the idea. I'm leaving the link out of this post because I want to test the premise rather than drive installs. Would you teach an agent to check for an endpoint like this before crawling? The weaknesses I see are publisher bias, incomplete indexes, and the need for agents to verify claims independently. Adoption also seems hard unless agent runtimes agree on discovery. Does this solve a real retrieval problem, or duplicate llms.txt, MCP, and normal browsing without enough benefit? I would especially value objections from anyone building browsing or research agents.