Search engines appear to care more about being good "Netizens". It's not like GoogleBot never crashed a site, but it's rare. Search engine bots check if they need to back off for a bit, they check etags, notices if page changes infrequently and slow down their crawler frequency.

If you train an LLM, it's not like you keep a copy of every page around, so there's no point to check if you need to re-scrape a page, you do, because you store nothing.

Personally I think people would be pretty indifferent to the new generation of scrapers, AI or other types, if they at least behaved and slowed down if they notice a site struggling. If they had the slightest bit of respect for others on the web, this wouldn't be an issue.