I've learned that the ability to extrapolate the positions of moving cars unconsciously and effortlessly is not one that all humans have, so maybe my confusion comes from the privilege of having that ability, but...

I don't quite understand this complaint. Usually, upon approaching a roundabout, I look slightly to the left to ensure that it's clear to enter. Even if it's busy, and I have to come to a complete stop, I just have to look out of the side window, at worst. I have never encountered a roundabout that required looking over my shoulder to see incoming traffic, and I used to drive a cargo van that actually made that impossible. In any case, once it is clear to enter, then I can shift my focus ahead again. There's no longer any reason to look for traffic from the left, since there isn't any within range (that's what waiting until it's clear means), unless a driver has instantly accelerated to dangerous speeds.

That's one of the things that I like about roundabouts: I only need to look in one direction at a time, unlike traditional intersections, where I need to look in at least 5 directions simultaneously for a left turn: 1) oncoming traffic, 2) oncoming pedestrians, 3) same-direction pedestrians, 4) possible cars from the left, and 5) possible cars from the right.

Roundabouts are deathtraps. The reason they "work" is that they're so obviously deathtraps that even blithering idiots realize it and slow the fuck down.

"Work" is also in quotes because their throughput is so much less than a proper intersection. Roundabouts put zero effort into preventing starvation of a particular route.