In the end its not the crypto that makes it more secure. Estonia still has a national identifier number, just like US has the SSN. The difference is that while I can know your name, DOB and the identifier (which actually contains your DOB in it), I cant easily pretend to be you. And this is because the process itself is different - when I got to open a bank account, I present my ID card, the bank can plug it in and pull up my profile from the central authority (ran by the government), and I need to pass the checks of being there in person, with a matching ID, which also checks out from the central system (including picture).

Combine this with for example strong proof via blockchain about who used to check your info and from where, and you are at a pretty good spot. Note that Estonia does not do that last part just yet.

As for the US, the chances of having a national ID card along with similar infrastructure are slim to none. So don't hold your breath about major changes any time soon. The best best would be to get closer to something like the above solution via private companies or maybe the credit bureaus themselves (once they are force to change their business model from aggregating and selling data without your consent).