Matthew
If you are using monofilament bristles you are rinsing the dirt away whilst you are cleaning – because the water, and loosened dirt, drains through the bristles throughout the process.
Rinsing IS a waste of time if the windows haven’t been cleaned properly.
If they HAVE been cleaned properly, rinsing MIGHT not be necessary - but I wouldn't risk it.
Personally, I concentrate on the CLEANING, with particular attention given to the tops and corners. After that, I find that a QUICK sweep from side to side (starting at the top and zig-zagging down to the bottom) is all that is necessary.
A word of warning, however, from my own experience:
Sometimes, windows don’t LOOK dirty at all and it is natural to think that a quick operation will suffice. On such occasions, I always have a quick look before leaving the premises and have been surprised sometimes to find that I have needed to re-do some of the windows (properly the second time!), so that in the end, I didn’t save any time at all (probably took me longer!).
Mike