My experience (N=~5) is that the waiting times for legevakten are in the order of a couple of hours for anything non trivial. I have also observed some reluctance on preventative tests at the fastlege.
I don't mean to contradict your observations, but our experiences could have been different based on our age, location, gender and what we're being treated for. Selecting a good GP matters a lot too.
> they do the required tests and examinations
Do you have a source or is this anecdata? I do agree with your other claims though.