It's only crossed by the same amount of drivers than a regular intersection: those going on the same street as you.

"They are all driving at full speed"

Actually no, the curve of the roundabout (for properly designed roundabouts) slows them down. In fact a traditional intersection causes them to drive even faster since many drivers go in a straight line.

"It is a delicate game"

The nice thing about roundabouts is that you only have to check for cars coming from ONE direction, as opposed to a traditional intersection where cars can come from behind you, from your side, or from in front of you. So crossing a roundabout requires less cognitive bandwidth.

At lower-traffic intersections the difference is less pronounced, partly because it's easier to force your way across even without a signal, and partly because the signals at less busy intersections may not give pedestrians an exclusive period in the cycle anyway (e.g. by allowing left turns on a regular green).

This might be Copenhagen-specific, but in Copenhagen I also find roundabouts make the pedestrian/bicyclist interaction less clear. At regular intersections, bicyclists can't cross your path when you have a walk signal, but at roundabouts they seem to just go through and are less likely than cars to stop preemptively when they see a pedestrian wanting to cross. Roundabouts aren't very common though, so maybe this would be worked out if there were more of them.

You may find them nicer, but they are not safer. The data already shows roundabouts are safer. As the article reports: "researchers have found that roundabouts reduce [...] pedestrian/cyclist incidents by 40%"

Sweden takes an interesting approach in combining both. There are a lot of roundabouts, but most of them also have a signal at the entrance. This makes it easy to cross as a pedestrian, because your crosswalk at the roundabout entrance is protected with an exclusive signal cycle. That forces a gap in traffic instead of you having to force the gap by trying to step out. Possibly even safer than either option alone?

In both cases, traditional or roundabout, drivers are supposed to leave gaps in the traffic to at least let some cars through the intersection.

In both cases, if drivers don't follow that rule gridlock will ensue. In fact, 2-3 cars stuck in the middle of a traditional intersection is often all you need to completely block entry and exit traffic by preventing anyone from going straight or making left turns: https://en.wikipedia.org/wiki/Gridlock

I always found it funny how easy it would be to DDOS a roundabout. Get 10 friends together and drive around in a circle all day.