Obligatory

There is a cool roundabout near me with stop lights that all turn red at the same time, stopping all vehicle traffic and letting pedestrians go.

I actually love them. Roundabouts have zebra paths on the lanes just before the roundabout themselves.

Same. They're wonderful for auto throughput and auto safety, that's about it. They don't save much if any space over traditional intersections (Really their space and shape requirements make them fairly prohibitive in any place that isn't already dominated exclusively by motor infrastructure), they create a lot more travel distance for pedestrians and cyclists who have to go around the outside, and they generally don't have any signals for cars to stop for pedestrians and cyclists crossing as they make their way around that long orbit. They're about as effective a solution to our car-centric society as the electric car.

It sounds like you have only found badly designed roundabouts to be honest. Not Just Bikes probably has a video dedicated on how a good one should look like, including priority signaling when appropriate

I would like to add, that a roundabout where people who are trying to exit have to stop for pedestrians, make a very unsafe roundabout.

Sure, people entering should stop, but if cars exiting have to stop, it makes too many points of failure. Cars exiting already have to watch for bikes over their shoulder, while also looking ahead to make sure the car in front of them isn't stoppinh for some other reason. If they also have to look for pedestrians crossing, their attention will simply be too divided in too many different directions.

Instead a pedestrian crossing needs to let cars exit, and cars entering need to give plenty room for pedestrians to cross.

This is very possible to make intuitive and easy through design, that puts to crosswalk about a cars length away from the entrence to the roundabout. That way, cars about to enter can focus on other bad driver incapable of signaling, and cars waiting in line can focus on pedestrians.

Unfortunately I have only seen about a handful roundabouts designed that way in my life here in Europe, but they make everything much better for pedestrians and cyclists.

And when there are lights it takes so long to pass through them because you have to take a huge detour around the cars and wait at multiple lights.

Yes. From the IIHS:

Studies in Europe indicate that, on average, converting conventional intersections to roundabouts can reduce pedestrian crashes by about 75% (Brilon et al., 1993; Schoon & van Minnen, 1994).

Are bikes presumed to have right of way or do both cars and bikes slow down and wave each other on? Or is the concept of slower moving vehicles not always having right of way a uniquely Yank phenomena?

That looks like a great way to get hit by a car

What the fuck is that?

Yeah Ohio has been slowly switching to roundabouts for over a decade. Then i moved to the PNW where they're definitely slower to making the switch but still doing it.

Major intersections it's still rare, but I've lived in a small town where the primary intersection was a roundabout

Get RAMmed!

It depends what we are talking about.

That's not necessarily the case, and depends on a lot of factors. They're generally great for cyclists. For pedestrians it varies.

Just make it analogy with a gun barrel or something that kills kids and they'll understand.

We have plenty of roundabouts, but we also have other alternatives, and many that work better.