Geoff -
It's an entirely different mode of operation.

One is flush-n-wait ("my" method"), the other, as you describe, is flush and, as you say, "wait a bit." A third would be flush-n-go, i.e. forget the "wait a bit."
I remain fully convinced that all three methods can be applied to any hx machine and, more than likely, a particular machine or the way a particular machine is set up will favor one method over another. In addition, a particular situation will favor one method vice another, like a barista jam

or perhaps the cappy loving in-laws are visiting
When you flush as you say, i.e. to "205 or 201", you are evacuating a goodly portion of the water in the hx. The hx is starting off from near ground zero, but you have succeeded in cooling off the grouphead only a certain amount. When you flush all the way down to 185 (or even lower), you have done a more thorough job of clearing out the hx. You are now even closer to ground zero as regards hx water temp and the grouphead will obviously be at a lower temp. Admittedly, you use more water but the subsequent shot or series of shots will be more consistent.
To change the subject a little - there's a lot of Vibiemme's being sold because of the thorough review process that's going on. Hopefully all of these Vibiemme's have thermosyphon orifices installed. If it's right enough for the V, it should be equally right for the G. This would dramatically reduce any cooling flush requirements but the recovery process would be slowed a little.