A prepaid SIM having the same security checks as a bank account definitely felt sour. And for some reason people think they have any privacy from the government.
My experience was in Germany. They checked my passport, face, name, address via PostIdent video.
Same procedure as with N26 and ING online banks, though the latter didn't work due to connection problems so I had to do it at the post office.
I like prepaid because I avoid contracts whenever I can. And I liked that I can get one fast.
I understand the reasoning - they can tie an identity to any SIM card and find you pretty fast if your number/IMEI pops up in some suspicious communications, but still, privacy blah blah.
This is the country that recently was against the EU wide chat surveillance directive that surfaces every few years now.
It really depends. Most prepaid phones require some sort of identify verification in the US. There may be a few that you can buy with cash, but i don't have the cash to find out which ones. I think it is also important to note that they are probably doing some sort of GPS and tower tracking, so even if you buy prepaid... activating it and what not probably discloses enough location information to help identify you.