Molly White also wrote about this in the context of open access on the web and people being concerned about how their works are being used.

“Wait, not like that”: Free and open access in the age of generative AI

The same thing happened again with the explosion of generative AI companies training models on CC-licensed works, and some were disappointed to see the group take the stance that, not only do CC licenses not prohibit AI training wholesale, AI training should be considered non-infringing by default from a copyright perspective.

If you don’t want to host your own data, take a look at TarSnap