I don’t know if you’re in the UK right now but I can tell you right now that I can go round the corner and buy a SIM card in cash plus a top-up voucher, from someone like this guy
https://www.coregroup.co.uk/assets/img/cards/independent-retail-sim-distribution.jpg
Aye, I’ve seen this misconception before and suspect it’s specific countries in the European continent where you have to register.