How do you know that that bot is part of those AI companies? Maybe it's my personal bot you're blocking, should I also not have (indirectly) access to the content?
You can use a honest user string denoting that it's your bot. Some AI companies label their bots transparently, they show up on the logs I keep.
While I understand that you may need a personal bot to crawl or mirror a site, I can't guarantee that I'll grant you access.
I don't like to be that heavy-handed in the first place, but capitalism is making it harder to trust entities which you can't see and talk face to face.
No. Access to my content is a privilege I grant you. I decide how you get to access it, and via a bot that my setup confuses for an AI crawler belonging to an anti-human AI corporation is not a valid way to access it. Get off my virtual lawn.