Not a civil engineer but as far as I know, the space is part of the point. If you keep the roads straight but just draw a circle in the middle, you don't have a roundabout. It only works properly if the drivers have to curve in and out of it.
You could keep the same space I guess by pinching the roads tighter near the entries/exits but I don't think anyone is talking about that.
The UK has mini roundabouts, which are just a painted white circle on the road: https://upload.wikimedia.org/wikipedia/commons/b/b0/Mini-rou...
Drivers treat them as a normal roundabout by giving way to traffic on the right.