I've now done this with most of my pipes, and I'm a convert too. I can't see doing it after every smoke because I'm lazy, but it'll be at least a once a week thing. Besides all the many advantages already mentioned, big plusses for me are: softens up the bad, soft cake for wiping out, leaving only the good, hard stuff behind; takes off wax, which I detest, and which the prior owners of many of my pipes apparently loved way too much; it seems to actually speed up resting/drying out after smokes, which I suppose is probably a byproduct of cleaning out residual tars and oils. After wiping them out and drying them off, I give them a quick swipe with a paper towel with a spot of mineral oil on it and put 'em in the rack all nice and squeaky clean and shiny. Beautiful!
The only "bad" thing that happened so far is that I had a shank extension on a Stanwell second (Danish Sovereign) turn from black to a kind of splotchy gray. I think it's made out of some sort of rubber, and the heat from the hot water discolored it. No oxidation-removal tricks are working on it. So, I guess back off the hottest water when rinsing pipes with cheapo shank extensions. I think I paid 15 bucks or something for the pipe, and it's never been a favorite, so I'm not heartbroken about it. Other than that, no problems whatsoever - all my stems look the same or better than they did before.