Thought experiment: You have a very large site with large amount of content. You allow Google to crawl your website and store a copy of all your content in it

Thought experiment: You have a very large site with large amount of content. You allow Google to crawl your website and store a copy of all your content in its cache. This amounts to hundreds of pages. That is, many pages of results in the Google search engine. Imagine for the thought experiment you later lose your website and all the content. Can you "crawl Google", e.g., site:website.com, to get it back? No. You will draw a ban. Google is in some ways like the Internet Archive but with some very peculiar rules. The Internet Archive encourages users to crawl it. Is crawling a special privilege that is only reserved for search engines catering to advertisers?