I've never skied without straps, up or down. It feels good to have them, naked without. But I'm open to changing if it's for the better. I see absolutely no problem skiing inbounds with straps.
Touring though, I can see how it could be very bad in an avalanche situation. The avalanche would basically take control of your hands if the poles get caught, preventing you from ''swimming'' to stay on top and would drag you under (all depending on type/size of avalanche). Also, if you're under and getting dug out, it's a pain to get the poles off and would save valuable seconds if there are no straps.
If you remember the video from the Grizzly couloir avalanche, there was one skier and one snowboarder caught near the top of the couloir. I doubt Mark (the skier) had pole straps on. He explained how he ditched one pole (and skis) and self-arrested with two hands on the other pole. He stopped halfway down the couloir and the avalanche passed him. He walked out uninjured physically. The snowboarder who was above him at the top, got dragged down all the way by his snowboard I'm guessing, having no real way to ditch it. I remember 15 years ago in Rossland, I met a snowboarder who chose to use hard boots for this reason: it would be easier to ditch in case of an avalanche.
All this to bring together another thing. Pole straps may fall in the same category as non-releaseable bindings such as the ones on snowboards, and people locking their dynafits.
Tree wells are easily predictable and I think it's very easy to avoid them. Dislocated shoulders? Maybe it would be an issue for people that ski with poles all over the place, but I personally don't see that as a possible problem if you keep control of your poles (same goes for broken legs and keeping control of your skis).
Avalanches are unpredictable. Nobody that ever got caught in one expected it. If the possibility of getting caught in an avalanche is the reason for not wearing straps, one should not wear straps for as long as one has his beacon on. That means for the up and down. No need to cut them off, just punch out the pin (or remove the screw) and remove the straps if that is your choice. You can put them back on at the hill.
I'm leaning towards removing the straps for touring. I know it would feel really akward for a while but as someone pointed out, you must get used to it, and grip your poles differently.
I think this is a good discussion topic, thanks for starting it.