Sure, things like Prime Music and Prime Video won't work due to licensing issues. But the traditional retail business? Now with Amazon Logistics taking over an increasing share of the last mile deliveries in established markets the legacy carriers like DHL could be leveraged for These markets. Maybe that will come one day.
Until then this absence of a considerable part of Europe presents a huge window of opportunity for Amazon-competitors. And even the same-day deliveries can be provided at least for metropolitan areas using third-party partners like DHL which have a tremendous amount experience in that field by now.
I assume that this window of opportunity will be closing in the near future, Amazon is pretty good in still being faster in closing opportunities than the competition is in exploiting them.
Regarding the geographical issues of Sweden in particular, some remoter parts of Germany, read islands, have the same issue. But right of the bat, next-day for the southern part of Sweden including Denmark should be doable. Same-day for cities like Stockholm largely depends on whether some one is Setting up a dedicated warehouse for that. And for the remainder of Sweden 2-day delivery shouldn't be too difficult to achieve.