The other take away points from GGT is that the same preflow-push algorithm can be extended to parametric problems (like the maximum-rate-closure problem that we are interested in) and still keep the same runtime complexity of O(n^3) for our FIFO-preflow-push case.
There is another interesting point to remember, which is the fact that we are interested in the min-cut set and not on the maxflow itself. So we may stop the algorithm execution earlier and possibly save half of the running time by doing so.