Google search is a monopoly not because of crawling. It's because of the all the data it knows about website stats and user behavior. Original Google idea of ranking based on links doesn't work because it's too easily gamed. You have to know what websites are good based on user preferences and that's where you need to have data. It's impossible to build anything similar to Google without access to large amounts of user data.
Sounds like you're implying that they are using Google Analytics to feed their ranking, but that's much easier to game than links are. User-signals on SERP clicks? There's a niche industry supplying those to SEOs (I've seen it a few times, I haven't seen it have any reliable impact).
