Let's pretend that age verification is a valid need -- is there a way using cryptographic approaches to viably allow an end user to prove that they meet the criteria without sharing other data that they don't want third parties to have access to?

In my opinion that is just mathematical obfuscation. They will not be able to resist the urge to have a random looking token that through some obscure process can be mapped back to a person. If not at first, it will appear in some update after people stop talking about it. Discord knows what people are talking about.

If that was a valid need, it would be solved entirely differently. ZK algorithms are a complete and privacy-preserving solution to that problem.

I find it impossible to believe that age verification services are rolled out for what they say they are.

I don't understand – what's the point of not collecting mass amounts of personal identity documents and face scans and linking them to online identities?

Yes, and it is very easy. https://news.ycombinator.com/item?id=46223051 "Flash a driver's license at a liquor store to buy a single-use token" And to save a debate, you can swap the phrase "liquor store" for "store" aka supermarket/grocery store.