Over the last forty years, I’ve taken a lot of different approaches to harmonic structure in my music. Each one has its benefits and drawbacks.
Tertian harmony has one amazing benefit that I don’t hear commented upon very often. More than any other method of building vertical sonorities, triads allow for an astonishing variety of embellishment.
Appoggiaturi, acciaccaturi, anticipazione — and that’s just the A-list. You can drizzle them all over a set of triads, with endless variation. But try using them with harmonies of other design, and you run out of options pretty quickly. A suspension on a quartal chord? Sorry, not going to happen. Neighbor tones around a cluster? Well, sure, but it’s not really the same thing.
So I enjoy using all kinds of vertical vocabularies, and, as I say, each has its benefits.
Pile up the thirds, though, and you can bet I’ll be going to town with those auxiliary dissonances.