Roundabouts do not need more space.

You can draw a circle on the road and have “roundabout rules” without the need for any car to even turn their wheels.

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.