No they don't, at least for Sweden. I remember when they regulated the market in Sweden (I was working for a gambling company at the time and I had to run the security & compliance for the Swedish license). There is no such thing as open market for gambling where the market is regulated (Sweden, Denmark, Estonia, not sure if Norway finally regulated).

As far as I know, a handful of companies got regulated at the first round, some failed and could not operate in Sweden (this might mean you actually need to deny access to users from Sweden - since you do KYC you know) for quite some time (before they eventually managed to get the license).

The problem (why the other user mentions all similar sites) is that the big companies (say Kindred group, Betsson) tend to spin up many alternative brands with different looks to attract different customers.

Also, most of the companies that operate in Scandinavia use the Maltese license, but that works only in unregulated markets (Finland, Iceland and Norway for example - unless something changed in the last 3 years). That said, getting a license once you have another is quite simple usually. The Swedish license for example is easier to get than and very similar to the Danish one, so if you operate in Denmark you can just fill in the paperwork and you should be easily able to pick that one up.