You assume that the proxy and the search provider follow these rules and do not cooperate in a different way (e.g. the proxy can send a query with an IP). But

You assume that the proxy and the search provider follow these rules and do not cooperate in a different way (e.g. the proxy can send a query with an IP). But can you actually prove it? The search provider isn't disclosed, we don't even know if it exists at all (as a separate entity).