Like the British, Australia has had roundabouts for at least five decades in some shape or form and there prevalence has increased over the last thirty years or so.
In the city were I live there is a five-way intersection and it is controlled by a single roundabout, nothing else. It's been operating for at least forty years without any issues.
It's easier and simpler to install a roundabout for such an intersection than to install a system of traffic lights.
Depending to the zealotry of the relevant traffic authority, if roundabouts are placed at every intersection on a major road for a considerable length of road, it can be very frustrating for drivers on the major road. In this situation the roundabout can slow traffic. Prior to the installation of the roundabout at those intersection the minor road intersecting the major road were controlled by Stop or Give Way signs, no traffic lights, and at when the major road was busy vehicles trying to enter the major road had very long waiting times. Hence, the roundabouts made the traffic flow easier for the vehicles on the minor roads faster and fairer.
As jhabbott states in his/her answer about, roundabouts can be small and cheap. A small painted circle and on the road and signs on the roads at the intersection informing drivers that the intersection is a roundabout. Even very large roundabouts can be virtually level with the rest of the road, allowing large heavy vehicles like buses and semi-trailers to drive straight through providing it is safe to do so.