It goes like this in the Netherlands as well. Typically with only a midwife, and a nurse if you want pain reduction medication because the midwife is not allowed to handle that. The exception is if there are medical indications like an early birth (I think before week 36), then a doctor would be present from the start.
Home births are a choice and a lot of people make that choice because it is a less stressful environment. We were told that the Netherlands has an above average amount of home births compared to the rest of Europe.
However for my daughter we were offered an even nicer option: There are special "non medical delivery" rooms in the hospitals around here. It looks and feels much more homely than a hospital room, has some normal chairs in it, the walls aren't white, it has a nice bathroom. You go there with your midwife that you already know from all the checkups. The process is like you describe it in Denmark, they indeed give you a lot of time to relax before and after.
But there is one thing different from home birth: It is right across the hallway from the medical delivery rooms, with full baby-ICU capabilities less than 10 seconds away and a red alarm button to press when you need medical help immediately. That was for us a comfortable feeling, because if things don't go right the natural way, you really don't want to be 15 minutes away from the hospital by ambulance.
Luckily we didn't need any of it, but the fact that it's there when needed feels safe.