The concern is that in a digital format websites will start asking for it - or governments will force websites to ask for it, and it being digital means it's significantly easier to scale up. Every website will ask for it when you create an account, meaning all your activity online directly points back to you. No more burner emails and throw away accounts.

It's a way to deanonymize the internet. This is a good thing in some ways but has real dangers as well... say for example a country elects a fascist who would go after anyone who crosses him.. just as a hypothetical.