I can see it happening if people start depending AI-generated proof libraries for the work they are interested in. Not because the libraries are proprietary, but because they are impenetrable. AI usage wouldn't result in this directly, but it could be a consequence of formal verification as a substitute for canonicalization in some cases.

(Disclaimer: I had quite a bit of formal training in mathematics at one point, but have worked in software for more than two decades now. I wasn't on the applied side, but I recall that MATLAB evoked similar concerns back in the day.)