If you can’t trust the government, the friction is irrelevant. They just generate a different primary key and don’t give it to you. Evil adversaries don’t play by rules. You’re just harming yourself in the good times and not helping yourself in the bad times. It's not like a government who wants to do real harm to individuals is just going to go whelp, no national ID, I guess we'll just go home and not hurt anyone.

If I were a hypothetical evil US government and there wasn't an SSN, I'd just create a database with an INTEGER PRIMARY KEY, compel Visa, MasterCard and American Express to send me 6 months of transaction history under a national security letter, correlate and quantize them all and presto, a few hours later, indexing complete.

It doesn't even have to be 95% accurate, although with some otherwise-anonymous looking demographics data you can get several nines of uniqueness. [1]

[1] https://dataprivacylab.org/projects/identifiability/paper1.p...