They've "fallen out of favor" totally due to marketing, and the BS pushed around by authors, "guides", and websites... that any fly reel must have brakes fit to stop a cargo plane, a "large arbor", and must cost a lot of $$$ or it is just not worth a fly fisher looking down his nose at. (unless, of course, it is a click-pawl Hardy, then it is masterful work of perfection, drag be damned....)
Nobody wants to remember that the original big fish and saltwater fly fishermen used Pfleuger Medalists modified with a leather pad against the spool to create an infinitely variable and controllable drag system.
I will say with confidence that 99% of people waving a fly rod will not ever NEED a high-tech drag, and don't have even an inkling of a clue as to how the resistance of their fly line in the water affects the resistance a hooked fish fights against, not counting the reel's drag system.
To the simpleton, proof does not matter once emotion takes hold of an issue.