Count me in the camp of an owner who does care about correctness. However, not showiness. I've ridden non gaited horses my whole life and have owned or ridden gaited ones too. While I don't show gaited horse, I do understand the mechanics and the correctness and how it relates to smoothness.
For example, my current horse is a RMH. When I decided to buy another horse I was looking at RMH, KMH, SSH, MFT, TWH, and Pasos because I already knew what they can do and what I had in mind. After deciding temperament was first and foremost my goal as I have a youngster now, I made sure to refresh my knowledge on the various gaits each one does so that when I was looking at horses I could spot which ones that were gaiting correctly vs those that were not, and here's why-
Back to my current horse-
When my horse is gaiting correctly (singlefooting) the ride is the smoothest he is capable of doing and it's a pure pleasure to ride. However, if he has ill fitting tack, is out of shape, whatever....he's going to do a stepping pace. Still more comfortable that a trot, yes and probably very impressive to some, but it is not as comfortable as singlefooting.
It's simple really...in general the more correctly (not showy) a gaited horse moves along, the smoother the ride will be.
Any horse, regardless of breed or gait, can accomplish a great number of things, but those things should be secondary to conformational soundness and moving correctly (gaited or not) for their longevity and health.