I don't think there are many 4-way stops in the US that cannot be replaced by a mini-roundabout for reasons of space or cost; mini-roundabouts are just solid white circles of paint on the ground, with a more or less pronounced mound. Their primary purpose is to trigger the right-of-way rules of a roundabout; often the junctions they are used on are too small to actually go "around" the mini-roundabout, in London (where I live) at least. Roads (and hence space for road furniture etc.) in the US are much larger than most roads in London.
A standard 4-way stop has two roads with two lanes each (both directions). No space beyond the widths of the road is used. They are very space efficient. It is also easy to build as an afterthought (just cross the roads).
I cannot find a roundabout design that fits into that same space. Looking at the Wikipedia entry[1], it seems much larger than a standard 4-way. Given the block patterns in American suburbs and housing developments, the extra space would eat into someone's yard.
Mini-roundabouts are much smaller; most UK roads do not have two lanes in either direction, so junctions are naturally smaller too.
A road with two lanes in either direction would normally be major enough to warrant traffic lights; or, if it's just a particularly wide suburban road, then the lane closest the pavement is often used for parking, and the road would narrow to one lane (with advantages in reducing speed somewhat) for a roundabout.
