I was never sure where I stood on the issue. A brief summary...
In the beginning, I was marginally against the idea due to arguments/positions held by some other posters which managed to convince me it might be bad.
However, I wasn't entirely opposed to the idea of damage on a 'miss,' because the concept of 'blunt force trauma' is something I am familiar with both from other rpgs and actual real life experience. Being hit by a weapon can still hurt even if your armor absorbs the strike. With that in mind, the idea of damage on a 'miss' didn't bother me because what exactly a hit or a miss is in D&D is abstract enough that it could easily be made to make sense.
Then I considered that it was possible to kill someone by missing in 5th Edition. While that's not exactly unheard of in light of what I mentioned above, it still seemed unusual compared to the rest of the game. I think part of my thinking here was skewed by abilities which were able to auto-kill minions in 4th; something about that bothered me.
On the other hand, it's not entirely clear what HP represent in D&D; if they aren't injury per se, then I suppose the concepts of hit and miss would be hazy as well, and maybe 'hit' and 'miss' don't mean the same thing in D&D that I typically understand the words to mean. (This line of thinking lead me to be roughly neutral on the subject because it supported the idea of damage on a miss being valid, but it brought up the idea that D&D is using language in such a way that what they mean is not obvious or intuitive -something I strongly dislike.)
I suppose, in the end, I just looked at the game and compared damage on a miss to the style of the game being made while also comparing the option to other options. A little bit of damage on a miss for one specific option of one specific class doesn't seem out of hand, and it's most certainly not broken when compared to other options; even other options from the same class. I'd say it's a touch weak when compared to many of the other options. So, overall, I support the idea of damage on a miss, but in very very small doses. I'm fine with one specific fighting style and maybe 4-5 abilities throughout the game which allow it when it seems thematically appropriate. I do not want it to be a general assumed part of the game overall though.