The credit agencies already attempt to verify you when you request a credit report ("did you ever live on Main Street", etc.) or put a credit freeze on so it's not a new problem for them.

But this leak presumably leaked all of that information as well.

The problem is using not-secret information as an authenticator.

For sure, I'm not saying this solves everything. I just think it would be a pareto improvement from where we are now.

Exactly why the whole system is broken.