The sim/operator is irrelevant for emergency calls, and the motivation behind keeping 2G is better signal reach for emergency calls. So I guess even if you wouldn't be able to call your friends from the top of the mountain, you could successfully dial or sms to 112 (if there's a distant mast somewhere in sight with a signal to camp on).
Not sure how it is in the EU specifically but many new networks around the world do not have 2G (Jio in India is (in)famously 4G-only, Tele2 in Moscow is 3G+4G)
Q: Do network operators/SIM card (re)sellers still have to support 2G, or just the phone manufacturers?