What's wrong with good ol' private keys?

PKI is a pretty old idea. People were trying to deploy it in the 90s. It turns out that managing the issuing and authentication of keys, as well as keeping them secure and if necessary revoking them, is such a huge headache that few organizations have managed to do it properly. It might be possible to do better now with TPMs in laptops and phones; essentially this is why Apple Pay is now slightly more trusted than plastic cards.

Same as with public transport. You can’t have because it’s haram for some political position

Nobody is anti-public-key crypto per se any more, the US government export control war ended long ago. It's just too much of a hassle to do the key management.

The ability to make an infinite number of them.

And that most people have no idea how to verify any ID, so they need a system that turns any given form of ID into a nice and simple "yes" or "no".

I'm not at all clear what kind of ID is going to be genuinely useful for video calls, given we should only be trusting existing contacts anyway? But those things are why "private key" isn't sufficient in isolation.

What's wrong with making an infinite number? You just need to check it against one public key.

Why couldn't a mobile app that everyone uses work for this. The person who wants to verify who they are uses the app, does digital signing and the other person gets notificatiom and the certification.

Sure, but that's basically the exact same value-add of Worldcoin, along with a bajillion other similar apps.