The issue is what this takes. You need:
1 document proving you are who you say (this cannot be a state or federal ID. I used my birth certificate, which can be difficult and time consuming to acquire if you don't have access to it.)
2 different documents from different sources proving you live where you say (this would need to be a bank statement or utility bill)
You must also provide a document proving your Social Security Number (this can be hard if you don't have the card - getting a new one is similarly painful), AND if your legal name has changed from what's on your birth certificate, you need to provide attestation of that (marriage or divorce paperwork, etc).
So you could potentially need up to 6 documents from 6 different sources, it's still up to the DMV to accept them, and you don't actually get the card for at least another 2-3 weeks at minimum. There's also a fee - in my state it would cost me about $80 after taxes.
They also don't stay in one place, and can just randomly show up in a place when you're, say, doing stealthy stuff. Suddenly assassinating a whole outpost of orcs becomes "aww shit, Feldûsh is here, and he's immune to stealth attacks" or '"oh no Roggvir just showed up, he's riding a warg and so are the other 4 guys he pals around with".