I assume "sport" may mean "cross training" and TMA may mean to "keep system pure" (it may not mean "cross training"). I also assume that we are not talking about sport such as boxing, wrestling, Judo, ... here. So the discussion of "sport" vs. "TMA" is really to discuss whether or not the "cross training" is necessary, or whether or not TMA is against "cross training".
There are many competitions within martial arts that don't need cross training, dependent on the rules. For example, if you are Kyokushin and want to compete in their championships you don't need to cross train at all. Same for TKD and a lot of others. Certainly if you want to fight MMA cross training is mandatory.
Here is a question. When your opponent tries to punch you, will you
1. block his punch?
Never, unless taken by surprise.
2. dodge his punch?
Sometimes, but always moving in as the punch goes past.
3. wrap his punching arms to obtain "clinch"?
Almost never.
4. enter to control and generally strike or take down (but the control is rarely a clinch)
Probably this over 90% of the time.
If you apply the 1st and the 2nd strategies, your opponent will punch you again.
Not with number 2 if done properly.
If you apply the 3rd strategy, what will you do after you have obtained a "clinch"? In order to continue after "clinch", you have to be good in grappling. If "cross training" is a must then "sport testing" is also a must. When you take this approach, I truly don't see any difference between "sport" and "TMA".
My idea of grappling is to control your opponent without your opponent controlling you. Cross training has absolutely no requirement for 'sport testing'. If you can't see the difference between sport and TMA, you haven't been paying attention. Hanzou's big gripe was that TMAs don't fight in competition.
We all know that it's better to use
- striking to against a grappler.
- grappling to against a striker.
Do we? In a sporting context maybe.
If you want to have both abilities, your will need to "cross train" and you will need to test your integration of striking and grappling in "sport".