Where do you live in Europe? This has simply not been my experience at all in France, Germany, UK, Italy and Spain so far. Online shops most of all don’t take debit at all and bricks and mortar shops will accept credit more often than debit. Again, my experience. And I prefer to pay with debit because I know the shop will pay less fees. I get refused at Starbucks, random shops in train stations, etc.

That is not correct. You may be thinking of a prepaid card or something like vpay. Debit cards are accepted practically everywhere.

Unless they have a direct agreement with a credit card company, most payment providers will give one-size-fits-all blended rate about 2.7% per transaction, even if it's debit.