If a crawler offered enough money they could be allowed too. It's not like Google has exclusive crawling rights.

There is a logistics problem here - even if you had enough money to pay, how would you get in touch with every single site to even let them know you're happy to pay? It's not like site operators routinely scan their error logs to see your failed crawling attempts and your offer in the user-agent.

Even if they see it, it's a classic chicken & egg problem: it's not worth the time of the site operator to engage with your offer until your search engine popular enough to matter, but your search engine will never become popular enough to matter if it doesn't have a critical mass of sites to begin with.