Well I have met some TMA instructors who had trained for a very long time, and couldn't fight their way out of a paper bag.
Anecdotes aside, I present exhibit A:
And exhibit B:
I do believe exhibit B had been training in Hung Gar for over 30 years....
Well the difference in Bjj is that shrimping for example has a direct application that can be used in a variety of situations. You can use the shrimp escape to get out of just about every bottom situation, and you use it constantly while rolling (sparring). I suppose a better comparison could be what we call the "triple threat", a series where you learn the Kimura (shoulder lock), Guillotine (choke), and the Hip bump (sweep) from the bottom of Guard. However unlike a kata, the application is practical and there is zero exaggeration. A student can learn the triple threat for the first time, and probably pull off a hip bump if someone was on top of him. Additionally, like shrimping, you use the triple threat set up constantly in sparring.
On the other hand, look at the Heian Kata series in Shotokan. The vast majority of those movements will never be used while fighting, and you never see them in the fighting form. However, in Shotokan we spent a lot of time perfecting those forms, and our ability to go up the ranks was based on our perfection of those movements in which we were never going to use. As I've said many times, my eyes were opened wide when I sparred a boxer in my dojo and all that karate training and pretty katas meant nothing.
So on one hand you have extremely applicable movements, and on the other you have a multitude of movements that aren't applicable to anything except getting a new piece of cloth wrapped around your waist. If someone asked me where they would go if they wanted to learn how to fight, it certainly wouldn't be a TMA.