This is already the case in most (all?) EU countries. Government-issued photo ID is required to activate a SIM card.
If you really need a burner you can still get one - there are people who activate SIM cards in bulk using their ID and resell them without collecting IDs. The practice itself is either gray area legally or straight up illegal depending on the country
I was a teenager when Switzerland introduced the mandatory ID check, in 2003 or 2004 iirc.
My carrier added 10 CHF credit to my prepaid plan for the trouble.
It's still fairly easy to buy a Lycamobile SIM/number that was enabled with a fake or stolen ID. Consequently some banks and services ban entire number ranges, which is not only ineffective but also affects people who committed the sin of keeping their first phone number even after moving to a proper postpaid plan...