The signup process has always been quite invasive for me. Is it possible get a phone in the states without handing over your SS, name, and DoB? I've never tried; what happens if you give bogus info?
I don't know about the United States as I've not been, but in every other country I've gotten a SIM it's been a matter of picking it up and the store and handing over money, same as if you're buying, say, deodrant. You can top up money anonymously too by buying prepaid vouchers.
I've certainly never had to hand over stuff like social security number (wtf?), but perhaps laws and/or telcos are different in U.S.
My family lived in Thailand when I was teenager, and this is how it worked there until just before we left (around 2013) there was a new law or something, and you actually had to physically go to a place, fill out a form, and show your passport just to get the stupid sim unlocked. At least in the US you can do it online or through the phone.
If you're careful enough it can also be reasonably anonymous.