Well you're about to see whether or not a fat tax works, because in a couple of years Denmark will have solid figures to show you. That's part of how evidence-based policy works. Try things, then a few years later, evaluate their performance. It beats banging to the drum of some blind ideal like "TAXATION IS ALWAYS BAD, AVOID ANY POLICY THAT INVOLVES TAX!!!11"
Yes, because this is the first time that a sin tax has ever been applied. >_