As mentioned, interchange fees are capped in the EU and UK, and the amount skimmed off by Visa and Mastercard comes out of this, so it's not the case that V/MC can take however much they want.I'm not particularly opposed to allowing merchants to pass on (some of) the transaction fees since requiring no fees at all be passed to the consumer means Visa/Mastercard get to basically take whatever they want from the retailer.
The interchange fee is what the merchant's bank pays the customer's bank. But this is only part of the total fee that banks charge merchants to accept cards, and banks can charge merchants whatever they want.
When merchants are not permitted to pass on fees, they would be incentivised to choose banks which charge lower fees. Whereas in somewhere like Australia where merchants can pass on fees (particularly when the fees are automatically added by the equipment and the merchant doesn't really notice them at all), merchants would be more inclined to choose payment processors that are easy to work with, etc.
So in theory, not allowing merchants to charge fees should lead to banks lowering their fees due to competition. However in practice it seems that at least for small/medium businesses card fees in the UK/Europe and Australia remain broadly the same at around 1-2%, even though the proportion that goes towards interchange (and thus Visa/MC) is lower in Europe.
I'm not sure why this should only be applied to foreign cards though - do card issuers charge retailers extra for these, as well as making money from currency conversion? I understand why the EU wouldn't let them charge another EU citizen more than a Danish citizen, but if the fees are such a problem for the retailers they they could legally surcharge everyone the same.
Well it's not about citizenship since Danish and other EU citizens would still face this charge if they have cards issued outside the EEA, and non-citizens with cards issued in the EEA wouldn't.
But merchants do get charged more when a customer uses a foreign-issued card, and even domestic cards defined as "premium" can attract higher charges.