I suppose since my country is very low population but very large I don't really see the problem. Everyone could have a house here and we'd still have plenty of room to space.
Sweden has a population of 10.5 million, ish, and an area of 447k square kilometres. Germany by contrast, has a population of around 80 million, and an area of 357k square kliometres.
That said, I believe low density can work just fine. You don't need highrises to improve population storage efficiency. Simple two-three story buildings work just fine too.
You could also lower the population, something modern society is managing just fine right now anyway. I personally really don't believe overpopulation is going to be a significant problem in the long run.