I don't think I agree. If we were talking about a game without bonuses, then yes. D&D has bonuses that can stack up pretty quickly, exceeding the standard deviation of the bell curve. If you're already above the hump, it's not a big deal. If you're below, though, you suddenly get even more bang out of each bonus.
I could be wrong. I really don't have the time to run a full statistical analysis, even though I think it'd be fascinating.
What I suspect would happen is that the PCs would hit even more often than they do now -- monsters are generally balanced by hit points, not AC. Meanwhile, monsters would miss more often -- even my casual players have annoyingly high armor classes. The net is to reduce the difficulty of medium to easy foes and (potentially) increase the difficulty of hard and extreme foes, throwing the idea of bounded accuracy out the window.
Also, close to 50% of all possibilities will come up with four results (9, 10, 11, 12) and almost 70% fit into six results (8, 9, 10, 11, 12, 13). For two 1st level characters, one with proficiency and one without, you end up with the sort of "skilled characters are skilled" result you presumably want. By the time you hit 10th level, proficiency ends up being a +35% bonus. That assumes a "fair" challenge is balanced at an average roll succeeding, whether you center it on proficient or non-proficient attempts. If you center it between the two, then you get the full peak of the bell curve and the bonus goes up. You might as well say "You succeed if you're proficient". There's no point in Expertise. If you start including easy modifiers, like bless, enhance ability, magic weapons, etc. things get worse.
In retrospect, what I really meant by "swingy" wasn't so much random in the specific sense. It was more in the sense that any given challenge is likely to be either auto-success or auto-fail. Again, I haven't actually run the numbers. If your play experience is different, that's cool. I just have a very, very bad gut reaction to applying 3d6 to D&D. I think 2d10 might be a shallow enough curve to split the difference, but I'm not sure.