This is my personal opinion and probably not the opinion of schooled riders or professional trainers.
I feel there is too much emphasis placed on how a gaited horse gaits. I don't understand why people who have gaited horses are so intent on making sure the horse gaits properly, unless of course, you are in the show ring. I don't get why people are so concerned about their gaiting horse if they are using them for trail. It is my opinion, that too many folks turn away from gaited horse breeds because they have been told they HAVE to learn to keep the horse in gait. Why? What is wrong with taking a nice trail ride in a plain old every day ordinary walk?? Gaited horses can do that but for some reason their owners don't expect them to, they expect more.
My older (11 now) Spotted Saddle Horse (aka Tennessee Walker) was obviously trained to get into a running walk as soon as the rider hits the saddle and asks him to move down the trail. I was rather frustrated with this and I wondered why they trained him in this manner. Then, after researching, I've discovered that's how gaited horses are often trained.
I have been spending the last four years, that's right, four years, working to get him to just enjoy a simple walk. A simple, ordinary walk. He's coming around, but he still has moments when he wants to bust into that running walk. All I want is a nice trail walk out of my horses. I'm not concerned with a running walk (maybe sometimes, but not the entire trail ride).
Bo is basically my lazy horse so for him to get into the running walk as soon as I ask more of him, well, that's my verification of how his previous owners rode him. I can see the change in his face as he believes I must want the same thing. When we go at a walk for a while, I can feel his relaxation because he's finally figuring out, I don't want all that other stuff from him.
Spirit is my younger guy and basically a clean slate. So, I haven't experienced this with him. He was entered in halter shows when he was two, before I bought him, but never trained to the specific walker gaits. I'm thankful for that!
Back in the early days of this country, when saddle horses were being bred and used to move people from one town to another comfortably, I doubt very many of those people concerned themselves about what gaits their horse could do. All they really knew was that the horse could move and they could ride comfortably for many miles over uneven trails and roads. It's only in the past 100 years or so, when horses were no longer used for transportation that people have put labels to the gaits. Now, that's fine if you're showing your horse and want to display all the gaits he can do for competition purposes, but in my opinion, if you want a gaited horse for pleasure riding and trail riding, don't get too caught up in whether your horse is gaiting correctly or not. Personally, my gaited horses will be walking down the trail and I'll be enjoying a great scenic ride, not rushing through it.