That's the only thing I would disagree with you on, that in general experienced or qualified people dislike Elixirs. I'm not saying this hasn't been your experience (because i'm sure we know different experienced and qualified people), but that mine has been quite a bit different.
I think a lot of it is contextual - I'm primarily a seven string player, so most of my discussions on the net have been with seven stringers and a good contingent of the players I know in real life play sevens, as well. A seven string guitar comes with its own set of problems, with regards to low end clarity - you need a fairly bright string with good attack to really reproduce that low B, something that's augmented by the fact that thicker strings tend to be darker and with a more compressed attack at a given pitch than a comparable thinner string.
So, Elixirs are a double win on a seven - first, right out of the box they're (and here I'm talking about Nanowebs - Polywebs are crap, the coating's too thick) a little brighter in fundamental tone than most strings. I know, that sounds crazy, considering all the badmouthing here about the coating, but try a .68 Nanoweb tuned to low B and compare it to a Daddario or GHS of the same guage. I've been told it has something to do with the core... Secondly, not only do they have a good attack when fresh, they also preserve it well. I can deaden a set of Daddario's in about a week of regular play, at which point the low end turns to mush and you lose a lot of low B articulation. Elixiers, I've gone several months - in rare cases, I've had strings still sound tolerable after 6 months plus.
Again, I'm not saying this makes them good for every single playing situation, just as you're not saying they're bad in every single situation either. I'm just tossing this out as an example that whether or not you like Elixirs isn't a factor of how experienced or qualified you are, across the board.
Personally, I love Elixir phospher bronze nanowebs on my Martin. I also haven't had nearly the breakage problem some of you have been talking about - I've had maybe one or two early breaks over the last four or so years I've been using Elixirs almost exclusively.