Not OP but I always found it odd that danish companies don’t post salaries in job ads. Just an observation vs the UK where it is common practice. Wondering if it’s one of the reasons, along with tax, salaries are so much lower in that country. Either way very kind of you to help OP, I highly recommend denmark as a country and culture.
Generally, the US does not. If they do for a higher paying position, I would find it weird and/or a sign that they aren’t open to negotiation, which I would take to mean they aren’t competitive (but that means you also have to be desirable enough to have options).