If your site is all about disseminating information (like Wikipedia), then Google would provide a free mirror of sorts.

If your site is about your product, Google won't be able to serve the sign-up page from AI; the traffic would come your way. Same for a site that sell something: the traffic you're interested in would arrive at your checkout page.

Paid-content sites and ad-supported sites are screwed though, on top of their being screwed by archive.is and ad blockers.