Surprisingly, I've often heard the following argument (except your point about space). Traditional intersections, despite being cheaper to install, are less economical from a total cost of ownership and all associated externalities perspective

The other benefit of roundabouts is they provide a much simpler situation for cars to encounter, since the intersection could be dumb and simpler heuristics should be able to resolve the management of traffic. A simple four way stop sign wouldn't be too hard, but I can't imagine trying to figure out much less optimize a complex highly trafficked 4 way intersection. A 4 way intersection basically forces you to coordinate centrally to optimize, instead of distributing the logic among participants in the intersection and only putting in central coordinating logic when traffic is very heavy. And even then, I'd expect it more to provide information to the vehicles entering about the vehicles already present and about to enter and letting the vehicles decide what is best.

I was going to write a big screed about how adding traffic lights and all the associated equipment would be much more expensive, then I realised you were talking about stop signs!

Intersections don't really have to be much bigger, and at minimum all you need is a circle painted in the middle of the intersection. Roundabouts work well when traffic flows in all directions evenly, but if not it's pretty easy to get into a situation where cars entering from a particular direction get screwed when there's lots of traffic.