Most checks are run as debits these days by most retailers. Those who don't have the tech, and don't want to deal with check fraud simply don't take them.
Walmart runs your check, but you get to keep it as your record. The system treats it like a debit card transaction.
Hell, when I worked for Autozone way back in the early 1990s, they had a check scanner that would red-flag checks where the account didn't have enough to cover the check amount. Run it through the machine, and if it's okay, accept the check for payment. Granted, it wasn't as quick as a debit card, and if they ran the account too low by the time the check actually cleared, it would be returned, but it cut out a lot of fraud up front.
I’m sorry, I was talking about wholesale business to business transactions. I doubt these rule changes will affect the retail situation much, as I’d doubt that many checks have been written in the last year in Denmark for retail transactions.