Flexion is a weird case because, again, the gnomonic projection is definitely an importal projection that is both useful for some practical applications and of significant theoretical interest, but it wouldn't be included in the Pareto front unless you include some metric favoring it. However, it's dubious if there is any value to "almost-gnomonic" projections that aren't completely so, although again, it's hard to judge because there don't seem to be any! Though that itself is informative: if this were a decent way to construct a projection, there would probably be some by now.
Well, I definitely don't think that "being tall and narrow" is, by itself, a worthwhile property to optimize for.
People seem to somewhat expect non-azimuthal projections to have a 2:1 aspect ratio. The plate carree and sinusoidal projections are like that naturally, and the Mollweide, Eckert IV/VI, and Hammer projections are arbitrarily defined to have it as well, even though there is no strong reason for it. Aside from meridian-interrupted projections, two-hemisphere projections (including azimuthal and hemisphere-in-a-square projections) also have a 2:1 aspect ratio when you put both hemispheres next to each other.
Projections designed to minimize distortion, however, tend to not have exactly 2:1 aspect ratios. The best-looking equal-area cylindrical and pseudocylindrical projections actually tend to have larger aspect ratios (compare Behrmann against Gall-Peters, for example, or Bromley against Mollweide), but the best lenticular projections (whether equal-area or compromise) actually tend to have smaller aspect ratios, as do cylindrical compromise projections (equirectangular with a standard parallel other than the equator, for example, or Gall stereographic regardless of standard parallel).
Even so, I would not consider aspect ratio to be important enough to put any effort into maximizing or minimizing it relative to other things, unless you just really need the map to fit in a particular space.
As a side note, Mercator is the most tall-and-narrow a projection can possibly get, since it has infinite height and finite width
It does not have especially low skewness, however. Presumably because of its extreme area distortions.