Compound exercises are the best workout for any sports (compound are usually strength exercises), thats why its the common workout plan for many athletes across many sports. When it comes to movement, be it charging an offensive line, or training sprawls, you use more then one muscle, so it would make sense to train them in the same fashion. Since compound uses more than one muscle, they allow you to lift more, which means you increase strength faster, and in more realistic proportion since these workouts are usually everday movements that can relate to other physical activities im sports and ma.
But, compound workouts do have their flaws. A bench press is known to hit chest (more of chest obviously), triceps and shoulders mostly, but many still need shoulder presses to force the shoulders to catch up, since a large part of the tension isnt hit by all the muscles at the same range of time. So, isolation is good if its to target lagging muscles, good examples are calves, which (for some, like myself) usually are hard to grow with leg workouts.
A common mistake in martial arts is that working out restricts flexibility. This is not true, its actually the opposite, since a rep usually flexes and stretches the muscle during the movement. Having huge size can hinder flexibility, which is another matter entirely, and even this has its exceptions (I'm pretty muscular to stand out on the beach, and I am inches from a full split).
Best workout is to do bursts workouts. Like training with a set time frame, for example, finishing a set within 40 seconds. This trains the body in releasing a huge burst of strength and endurance for quick bursts, and to rest, to repeat the process, which is good for wrestling, and point karate. Also, circuit training is good, it builds the above, but with more overal cardio/endurance training.
I changed to a strength training workout to add more power to my karate. Once my power numbers go up, i will switch to supersets (which is two sets done back to back) with more cardio since the higher in belt i go, the more people i am expected to fight back to back. I have to do what I can, considering I am one of the shortest people in my dojo.