I'm going to presume when you say strength training you are talking about the big three and a few other presses. I'm going to presume that you think any fighter not doing that is stupid. I believe you have claimed this before, but correct me if I'm wrong. Otherwise this post is dedicated to anyone else with that opinion, if not only to create a little nuance.
If we are talking about resistance training, obviously every martial artist is doing resistance training. As I said, I've never sparred with or rolled with a high level figher who wasn't very strong. Fighters have been doing strength training since the dawn of fighting.
Karatekas used to carry each other on their backs and use their surroundings to punch or kick or carry.
Wrestlers, grapplers and Judokais use each other as resistance and gymnastic like training.
MT guys and boxers do a lot of BW stuff and explosive work.
Just because it's not barbell work, doesn't mean it's not strenght work. They do thousand and thousand of resisted repetitions. It's not that fighters think they are special, they just know fighting.
Is max strength useful for a fighter? Yes. Can you build strength in many ways? Yes. Are there diminishing returns? Yes.
You claim that fighters are "special" but let's take a few other sports. Would you advice a swimmer to "just keep working on your PL total"? Would he need a 2xBW squat and 3xBW DL to be "good enough"? Would it be smart at all?
For a fighter, I'd grant you that it has to do with style. Someone like Lesnar, who needs to overpower people and take them down, has a lot of use for his freakish strength. Let's not forget he is a very good wrestler too, but I'll grant you that. Style has a lot to do with it. Now, as it pertains to this thread, let's look into size/strenght and punching power. Let's delve into striking:
Joe Fraizer was one of the hardest punchers all time in the HW division. Have you seen the video of him not being able to OHP 170lbs?
What about someone like Joe Lous? One of the hardest hitters ever too, but his training didn't include a heavy bench or DL. What about Marciano?
Let's take a look at Foreman. Now Foreman was a big guy. Let's compare him to a few big and strong guys.
Who do you think has the biggest bench, squat, deadlift, OHP and so forth? And who hits harder? I know it's very pidgeonholed, but bear with me. Foreman is one of the biggest hitters all time, obviously he hits harder. The amount of size and strength wont help the other guys. More barbell strength does not
necessarily equal more punching power. Now, let's take it a step further. Let's hypothetically say that Arnold and Brock could train boxing for years and years on end, without loosing their mass. Could they ever hope to hit as hard as Foreman in that case? Not a chance. This is only in the HW division, it's even easier to make a case in the lighter weight classes. Conor McGregor has more power in that left hand than anyone in the FW and LW division, yet he doesn't lift very heavy and isn't very muscular. He's strong no doubt though, but this again pertains to the one kind of training many of you guys deem sacred, heavy compounds. I know I'm cherry picking a little, but it's adding up to an argument.
I could go on with boxers for ages, but I wont. But I'd like to mention Thai fighters. How is it, that the Thais are the best in the world yet they are notorious for not doing any heavy strength training? Would that imply, that any foreigner could just add some heavy squats in their program and they would suddenly start beating them? Then why hasn't it happened yet? Surprise, surprise, the greatest Thai fighter ever didn't need to use heavy barbell training. If only he knew and didn't think he was "special":
You see where I am getting at?
I agree that grappling is a different beast, but even then there are many ways to Rome. Yes, strength is great, but as I said earlier, guys grappling and wrestling ARE strong. They are not some fragile weaklings. Not MMA fighters. We could lower the numbers are say that perhaps a 1,5xBW Squat and 2xBW DL would be reasonable before diminishing returns, but a lot of MMA fighters would be at that strength level already. Compounds are not some magic formula that works better than everything else in the world! It might not seem like it, but I actually like compounds. I do them myself, I think they are great tools! Easy to adjust and very straight forward. I'm not opposed to fighters doing them within reason at all. Quite the contrary. BUT the arrogance of claiming that it's the
only way and that you know better than these guys who's been there is not something I can agree with. I do both, so I know both worlds.