As a mma person I don't have to many issues with tma. The issues I do have, stem from the fact that, of the few TMA I have briefly trained, the training was way to easy.... Now I know I have posted in kata threads before I have learned much, about the nature of it, but the way some styles do kata is still odd to me. The mma in me thinks that instead of going through a set pattern that may or may not actually teach you anything, why not spend that time with a partner repping the moves your art contains?
I tend to fall in between on this. I primarily train in a TMA (we definitely sweat) but I also like MMA and think the live and wider spectrum nature it exposes can bring a whole lot of "reality" to martial arts training. When you are really getting punched, kicked, and taken to the ground... the stress level is much higher and you learn to think on your feet and control the adrenal response in a way that lighter and/or rehearsed sparring doesnt do... you also learn the importance of good basics and efficiency. Quite a bit of TMA training is theoretical and light-medium cooperative contact, and that "may" lead to some stuff getting taught and carried on that is pretty much nonsense.
I also think kata is very valuable, however I think the way some TMA schools teach them without exposing students to realistic bunkai and related flow drills is a bad idea. Students should have a good idea of the actual application of the kata they are practicing and have experience drilling some of the moves against others. Then you can take this back to the kata practice and visualize the attack while also working to perfect some of the kihon form.
Many of the best MMA practitioners have long histories and respect for the traditional arts. They need not be set against each other, but are actually great compliments.