Sadly the "legitimacy" you described is apparent in most dojo's around my area. Usually most of the dojo's have "striped belt systems", are mainly focused around their "little dragons" ages 3-5 program, and teach the actual art in a very limited way. I do aikido because there is no "sideline" programs that I have to deal with, just learning the pure art without screaming 4 year old black belts. The problem is most of the karate and TKD schools are focused around the whole "mcdojo" economic logic,not to say that that discredits the owner's knowledge of his own art, it just dulls the feel that you are actually learning something when 90% of the dojo is focused around teaching little kids as a form of babysitting. I almost cried when I saw a nat geo documentary of a japanese karate dojo, and their training and conditioning methods. Fact is you would get nothing close to that in America because the general martial art business has shifted from pleasing the customer instead of actually teaching them something
I am grateful to be have been invited to a semi-private dojo, that practices karate the kyokushin way, knockdown conditioning and always on mats: they are kind by being seemingly mean and punishing. And I have no doubt at the effectiveness of this dojo's training.
The reason for me to mention this is that if you seek sincere knowledge, is willing to "eat bitter" for real "gung fu" training, not just for pleasant pajama dancing yoga, teachers will reveal themselves, but be careful what you want, because you may get it.
aikido, jiu-jitsu, jujutsu, or judo people are impacting on the mat frequently and interacting with a training partner every class, but the training at a karate or taekowndo schools can vary greatly, but training in boxing, kickboxing, or muay Thai schools are fairly consistent, FWIW.
BTW taekwondo (TKD) or karate physics are very close, if not nearly the same. That WTF/Olympic TKD bobbing is a telegraphing way to spar when grabbing, face punching, and leg-kicks are allowed in a more realistic martial arts sparring dojang, not wearing hogu (WTF TKD chest/rib pads) - for example, no one in MMA, Enshin, Kyokushin, or kickboxing does that.