The countries I am familiar with in Europe (NL to name one) you can buy sim cards without any ID. Additionally there's at least 1 provider I know of that's giving them away for free while for the majority you pay 1-5 EUR but get some data after activation.
There's no limit on how many you can purchase at once either.
In Estonia, you could buy a prepaid SIM card in a convenience shop a few years ago, without any sort of ID verification. Not sure if that’s still an option but I think it’s not a priority there. You can then use it all over the EU.
And of course, buying a phone without a contract doesn’t require ID either.