I have no experience with it within the US but I did that in Germany (on LH though) It is so convenient, this is such a relief. I am really a fan of the old fashioned boarding passes but not to actually use them, just for my collection.

Other than that, the electronic BPs make it way easier. The only people that get confused are "our friends" at security. So far, I would be too scared to just show up with an electronic BP in the US, I would have a paper BP in my pocket in case I have a problem!

When I first used it, they handed my cell phone around at security because they had never seen that before I bet that day I could have gotten behind security without any problems and no real legibility to do so!