The main concern with age/identity verification tools seems to be the concern with storing your personal data for mass surveillance. Yet, their privacy policies say they'll remove it soon after the verification. Is the main pessimistic concern that they will not do that? And that it could be proved they do, age/identity verification wouldn't be an issue?

No the main concern is building a system where the government gets to decide what you can or cannot view on an individual basis.

Bing Chat suffered the same fate

Tbh I never even heard of that!