This is odd to say when the YouTube algorithm has been proven to push right wing propaganda.
The concept of "conspiracies" is a bit off. It's not a "conspiracy" when Bezos kills the Washington Post's endorsement of Harris, or fires journalists who criticize him. YouTube doesn't need to remove a video if the algorithm never shows it to anybody.
It is kinda crazy to imagine a secret cabal of rich people who surreptitiously run the world, rather than the well known cabal of rich people who openly run the world.
You answered your own question. The search engine indexes your page to send traffic to you. The AI bot indexes your page to plagiarize your content.
Anecdotally, AI also routinely ignores sites' robots.txt and spoof their agents to try to hide what they're doing. A lot of site owners are complaining about the costs of delivering content to web scrapers. Where search indexes might hit a site every day, some AI bots are running every hour and just wasting their bandwidth.