This seems incorrect. I've traveled around in EU and haven't seen a single ID check for SIMs yet. Where is this happening? In my home country of Estonia we even have SIMs being given away for free on the streets as advertisement.
Germany (O2) had an obnoxious check. The dude bitched at me because I had a copy of my passport "saved in the cloud" (it was in 1Password local on my phone; given that the US, RU, CN, JP, UA, MY etc governments all have copies of my passport already, it's a whole lot less sensitive than anything else I have in a local-only encrypted database on my phone. It took about 30m to go through the process.