I use them.
A. I've not had any sort of thumb injury or sprain since switching to the pole strap technique where you put your hand up through the strap and then put your hand on top of it. That way, your thumb doesn't get caught and voila - no more thumb strains. You let go of the pole and they dangle freely from the wrist.
B. When my poles get stuck on a branch or something - the straps are loose enough that they just slide right off my hands. I've never had a shoulder strain, and sometimes barely even feel it. If I had the straps tight, that would probably be different.
C. I've read things that said, if you're caught in an avalanche your gear can weigh you down, and others that said it helps you to float. I've read things that say you should try to "swim" and more recently an article that said NOT to try to swim, but to try to keep your hands in front of your face to maintain an air pocket. Knowing that when caught on something, my pole straps come off my wrist much easier than my skis come off my feet... I don't worry about this. To me -- if I think I'm in that dangerous of avalanche terrain that my pole straps are going to make a difference... I need to just turn back around and get out of there. Now, I understand that if you're running a business, and have legal liability issues, why not have your clients take their straps off? It's something you can say you did, and whether or not it actually does any good, it looks good in a lawsuit case to have a policy on the matter. Personally, I just go touring on my own (with friends), and when conditions are pretty safe, and I don't worry about my poles making a difference in an avalanche situation.
Why DO I wear them? Because I've stuck them in the ground while poling along the high T on a powder day and they stay there and I'd have lost them if not for the strap on my wrist, but they come off when they get stuck on something more solid, like a branch. I'm not missing out on my first tracks for a pole stuck in the powder. Especially when I don't really see any downside to using them (when they're loose anyway). Plus, I've found them to be helpful in the event I need to self-arrest.