Just to note;I don't follow BB'ing so don't know Mr James or his MTUT system...I searched it.
Been pretty much established that quick hard muscle contractions (positive rep...shorting the muscle) followed by a slower eccentric (negative rep...lengthening the muscle) is the best way to increase muscle strength and size. Of course there are exceptions like with anything else in training. Mid range & partial reps come to mind. And the once trendy 3.1.4.0 (just an example..other forms of this) exercise style.
There are also seldom used negative only reps, where much heavier weight is used, with very slow lowering. Negatives are a great way to increase the strength in chinning/pullup movements.
Just my view: Super slow reps are usually done in 8-12 rep range, moderate weight and in strict style. They can be a good protocol to obtain a certain level of development and strength, and can be joint friendly. But for the average BB'er, with the intent to get much bigger and stronger, slower and strict reps just don't seem to accomplish this aim. Now the MTUT may work wonders for a select few, and that is a good thing. Only way to find out is to try this style of training, giving it a fair chance, yourself. You may be the exception to the rule. As yet, I have failed to see a large, impressive and strong BB'er ever use anywhere near the super slow style of training, or even strict reps. They usually hit the middle range rep scheme only and at a very quick pace. Semi to extreme cheating in the process. It's the TUT (Time Under Tension) thing mostly.
Rehab requires slower movements because the muscle area is relearning to call upon the proper muscle memory/impulse to complete a normal function. Also the tendon/ligaments healing comes into importance. Light stretching, and massage, is also a major element to take into consideration in any healing process. Can never rush a injury. Cold laser theory seems to becoming more of a medical aid, of late.
Good Luck