Well, that will work indeed. The most popular anonymous ATM brand in EU seems to be ShitcoinsClub (or Bitomat as their rebranded name goes). From my experience their fees for selling you fiat for crypto vary from 0% to 10%, most of the time around 4-5% or so. It should be possible to buy at 2-3% if one is patient enough to wait for the low prices.
Still, as you mentioned the anonymous crypto ATMs in EU will work till the end of 2025 or so. After that MiCA and the other regulations will kick in and everyone will require a KYC.
In fact, shitcoins.club has introduced the kyc for all transactions in Spain since 1 January this year, ahead of the entry into force of the law, so I doubt very much that they allow to operate without kyc in any European country subject to the MiCA today. The rest of the bitcoin ATM operators remain the same.