The ID presented at time of purchase does not have to be the ID of the actual user of the card. Your local drunkard will be happy to get $10 to buy a SIM card for you. Or you could visit eBay (or local equivalent) and get a valid SIM card without leaving your house.
"For the Selfie-Ident you identify yourself with your identity card, passport or residence permit. (Selfie-Ident is currently possible worldwide with the German ID card, residence permit and passport. Alternatively, you can use Video-Ident and identify yourself in a video call with an employee.)
Important: Temporary identification documents are not supported due to internal check. You need a tablet or smartphone with a camera and an internet connection."
In my country, giving a SIM card to another person who does something illegal, is a crime. No doubt EU might soon have the same law - they are pretty good at copying.
As a result, sites where I could rent a number for verification, now don't offer local numbers anymore.
Even with fair usage policy violations (like long term roaming) the prices are still quite reasonable: 1.30 EUR/GiB (+VAT); from next year 1.10 EUR/GiB (+VAT).
The only thing that happens is your data becomes a lot more expensive, the card still continues to work as normal. I've not lived in Poland for over 15 years now, and I still have a polish SIM card that I use almost daily - the only thing that I've lost due to roaming long term is cheap data packs, I can still call and text as normal from my monthly allowance.
There's eu(maybe even EEA?) wide free roaming legally mandated since I think 2017 or so? But it's not a permanent solution, your second paragraph still holds true.
As far as I know it is only EU. Both UK and Switzerland have some operators that roam and some that do not. fwiw, fastweb in Italy provides roaming in both and has a very generous fair usage policy.
That's because we are no longer in the EU. Before Brexit they were legally mandated to allow free roaming in the EU. Now they are back to charging whatever outrageous prices they wish.