I see what you mean and I have 3 great examples of MT vs counter-striking Karate which show a wrong approach and a correct approach.
1. WRONG APPROACH: Thiago Silva vs Lyoto Machida
Silva kept the pressure on Machida but wasn't very explosive. Instead he just plodded after Lyoto, throwing slow power shots which got him countered badly, knocked down and finally KTFO.
Nothing to add here, horrible strategy, horrible execution, horrible result.
2. ALMOST CORRECT APPROACH: Rua vs Machida 1
Rua was cautious and did not charge in blindly since he knew it wouldn't work against Lyoto. Instead Shogun focused on MT's signature weapon - the low kick. The idea was to damage Machida's legs to take away his key tool - mobility. Of course low kicks still leave you open to counters so the fight turns into a game of timing and speed. Rua landed plenty kicks which slowed Machida down very much in the last two rounds but he also got countered to the head many times - and this probably swayed the judges.
Valid strategy, especially if your kicks are lightning fast and your chin is made of rock. Unlikely to get you a finish tho and since strikes to the head *look* more damaging / impressive you may end up on the wrong side of a close decision.
3. BEST APPROACH: Rua vs Machida 2
Counter the counter! As you can see in the gif below Shogun really studied Machida and must have spent weeks analyzing their first encounter to prepare such a brilliant counter. I am myself a very devout Machida fan but I have to give Rua huge props for his rematch performance.
Obviously this approach requires amazing skill, speed, timing and a very deep analysis of the opponent. After Machida's loss it seemed like "the riddle was solved" and the strategy was now evident. Perhaps it was and many fighters tried it but even top dogs like Couture, Hendo and Mousasi couldn't do the same.