The only double diamond I routinely encounter (and just realized that’s what it was) is around an interstate interchange. With the scale of the interstate traffic, roundabouts would be difficult to use.

Difficult, but not impossible… I’ve also used roundabouts over highway traffic, but not with the same throughput of traffic that interstates have.

It's a matter of max throughput. The diverging diamonds is great when we are talking many lanes in all directions anyway, like in highway interchanges. The roundabout wins when max throughput is not the goal, and some of its side properties, like some mild traffic calming and better interactions with pedestrians come into effect.

They aren't really in competition with each other under most circumstances. It's like comparing bicycles and trains for transportation.

Roundabouts are not inherently load-balancing. If you drive on the right, so counter-clockwise around the roundabout, and there's a dominant south to north flow, you won't get a fair share when coming from the east.

East can only enter the roundabout when there's a gap, and if the south to north traffic is coming from an event, or a roro ferry, it's going to a lot of waiting. A traffic signal that's in event mode isn't going to give the east entrance much time either, but it will have some limit, most likely before the capacity of the ferry or the ballgame parking lot.

Lots of roundabouts have traffic lights here in the U.K.

See here for e.g. for a large one that intersects several major roads: https://maps.app.goo.gl/51sQeVa4ozSQgW9U6?g_st=ic

Don’t take this the wrong way, but Americans seem to have an issue with roundabouts. I’ve seen several go in around LA and then promptly get turned into wacky stop signs. Btw I am American, though I’m living in New Zealand and I prefer roundabouts to stop signs.

They're not better, they serve a different purpose: primarily for highway access from an arterial. You're not going to put a roundabout on your highways, and both roads can expect to have the highest level of demand on throughput.

In Spain they managed to make roundabouts with traffic lights. It's not uncommon but having traffic lights on small roundabouts can make roundabouts very hard to navigate.

Roundabouts have low capacity