Collaborative environment meaning that any PFY employed by the "AI" providers can read your most intimate thought processes and keep track of embarrassing failures or misconceptions.
Though by your "Perelman and Wiles didn't need "AI" assistance" comment, you'd surely be there on the sidelines to ridicule them for each and every single one. I guess maybe that's where your concerns are coming from?
I can practically see how these concerns of yours would suddenly evaporate if they started using self-hosted models instead... ... yeah, right, who are we kidding?