I live in the UK, which has roundabouts, mini roundabouts, double and triple roundabouts, traffic-light controlled roundabouts, and magic roundabouts. They work perfectly fine.

The difference is that traffic flows very differently in the UK to the US. In fact, the way traffic flows in those two countries captures a lot of their cultural differences. In the US, everything needs a grand overarching theory and imposed order, which is why Americans need traffic lights, and why they’re so keen on a very specific set of liberties that allow them to freely live such similar lifestyles. The UK embraces mild chaos and ruthless pragmatism, with everyone finding locally optimal solutions to their own problems, so things like roundabouts fit well with the national mindset.

I agree with this, and I'll offer a rationale.

Because the US largely "grew up with cars", the economy was built around the expectation that folks can drive to work. The population density of the US reflects this, and mass transit just doesn't work in small/middle America. That means everyone needs to be able to drive. If you can't drive, you can't work. That isn't the case in the UK, and you'll notice a lot of these "driver beware" analysis is explained by the fact that driving in the UK is seen as a privilege whereas it is a right in the US. This sort of "mild chaos" is prohibitive for a lot of would-be UK drivers, and they just take the bus.