I guess jaywalking stuff makes this harder? Because in the UK for example, roundabouts will often be surrounded by marked areas for pedestrians to cross, but they are not proper crossings. You don't have to wait or expect traffic to stop for you, you just walk across when it's clear.

And as a pedestrian, drivers going around a circle aren't necessarily going to see you until they're already exiting, even if the city didn't put something large in the center that entirely blocks their vision. Plus, you lose the ability to know which way a car is likely to go until it's already too late.

When I lived in Nashville, I spent a lot of time near a roundabout, and even after they redid it to be a bit better I still had to avoid it for my own safety. The light-controlled intersection next to it was much less of a problem.