Portugal is in the EU so how come CC fees can exceed the EU maximum which is a fraction of a percent? (and likely less than the cost of cash handling for all but the smallest merchants).
I suspect you're misunderstanding that that limit applies to. Until you are taking substantial revenues as a merchant, you are surely going to be paying more than a small fraction of a percent in credit card processing fees one way or another.
Small merchants probably pay north of 2-3% to some intermediary provider (I hope a future regulation will cap this as well). I still see almost no merchants that don't take credit cards here though - likely because when card use reaches a critical mass you 1) lose too much business if you don't accept cards (I can go 6 months without touching cash) and 2) The amount of cash shrinks to a point where there marginal cost of the next cash transaction is also pretty high, e.g if you do 1000 card transactions and only 10 cash transactions in a business day then each cash transaction has to carry 1/10th of the cost of cash handling for the day.