Queue time is the usual explanation for why rentals are hard to get. It doesn't hold everywhere — in several kommuner other things decide.
In the metro regions, queue time is nearly always what decides. But Sweden is bigger than that, and across a substantial part of the country other things govern who gets the contract: income requirements, move-in date, and how fast you reply.
That's especially true in towns with a university but no acute housing shortage, and in kommuner where new building has outpaced population growth in recent years.
If you can move, it's worth looking wider than the three biggest cities. Watching a town you hadn't considered costs nothing to add.

