They aren't, but the problem is that open problems tend to emerge when people are working on other problems. If fewer people are spending time deeply thinking about current problems since a handful of labs are solving them with AI without an eye towards understanding and only on verification, the pool of open problems won't be continuously growing. There is a fear that there will be a chilling effect on the community if people are disincentivized from trying to solve deep problems or study them for understanding as opposed to simply focusing on verification. It's more of a social and community problem than a fundamental problem with mathematics itself becoming "completed".
So we can let the ai generate some math problems based on the solutions found? Other fields (computer science, physics, ...) can generate math problems too.
tl;dr - it's content creation rather than process and understanding
That explains a lot on why his arguments always focus on the "social part"