For a human, using a sponge and squeegee combo is probably the most effective way to clean a window. For a robot, I would imagine that the answer is something more like a pressure washer, with a hood which covers the work area and reclaims the wash water. The water would then be filtered and reused until the particulate count rose too high, at which point it would be flushed and replaced with fresh. A sheeting additive would be used to cause the water to run off without spotting.
This probably wouldn't replace human window washing entirely, but it seems like it has the potential to replace at least some of the washes.
I've often wondered if anyone has ever tried a project to make a building which washes itself, using a robot designed for the building, and a building designed for the robot. I can imagine many problems with such a project without even undertaking it, mostly related to critters taking up residence in the mechanisms and/or tracks, but if it operated continuously that might well eliminate some of those objections. A universal window washing robot has a more complicated task than such a device would.
Did you even read the article? You'll find it discusses how the old World Trade Center Towers had built in devices that were made specifically for the building that would automatically go up and down cleaning it. The only problem was they missed the corners and creases of each pane and the rich people at the top of the building didn't want the grimy borders to their new expensive view of NYC.
It sounds like you have a lot of ideas for building a nice big heavy expensive machine that moves up and down a building. Burst forth and implement your idea, I think you'll find that the the weight, the power and the water feed to these devices will push you towards what has already been implemented and did not do a satisfactory job. Humans had to follow up behind the built in robots to clean spots they had missed.
It's funny, I read articles on Slashdot about how AI is the one thing that threatens man. And we can't even implement AI and pattern recognition to replace a window washer -- oh the incongruity!