I'd argue that savory cocktails are about the interplay between salt and umami. The primary taste in a martini, of the five basic tastes (sweet, sour, salty, bitter, umami), is umami. White vermouth is basically umami; gin has a good smattering of it; green olives have a good chunk.
I think the reason people like "extra dry martinis" -- ones which limit, or even virtually eliminate, the vermouth -- is because they get overloaded with umami. It's an aggressive flavor, one which I quite like, but, like any flavor, "too much" is too much. It can start to strike one as "oily" or "greasy", even. I go heavy on the vermouth in my own martinis -- but that's because, remember, as sensitive as my NOSE is, I've got fewer taste-buds per inch than most of you, so, for me, I punch up those five basic tastes.
xiphias titled his article "Some thoughts on savory cocktails", so now I'm wondering about herbal cocktails. Maybe not parsley, but sage, rosemary, and thyme.....
Would a curry cocktail be tolerable?