Everyone can only train 'part time' short of top level professionals. And the ones who care about being good include some strength and conditioning work, without variation. You cannot possibly disagree with this. They include it because it is worth it. A strong fighter is better than a weak fighter, even if the strong fighter has to forego a small amount of skill training for a certain time period. But yes, every fighter who wants to get good finds some way to include strength and conditioning. It's a necessity.

Go find a high level wrestler your weight and tell him how much your pumping iron matters for what he does. Get on the mat and see what real strength is. I'm not even just talking about technical domination, dude will physically overpower you to the point you feel like a bitch.

I can overpower and exert my will rolling with people who are more experienced than I am if I am significantly stronger than them a good portion of the time.

Having skill is of top importance but between two people of the same skill the stronger one will always win.

Recovery and injury prevention are absolutely paramount, but you think the guy needs to be further breaking himself down when he could be recovering.

This has been the mantra of ignorant strength coaches around the world forever. "I don't want my players deadlifting, they get beat up enough on the field!" But like it or not, getting stronger in the weight room makes you more resilient on the field, or the mat, and leads to an increased improvement in performance enough to make it worth while. Obviously there is a point of diminishing returns, but negating strength training altogether would put you at a huge disadvantage, and make you an anomaly in terms of top level people, as they all find some way for physical improvement outside of practicing their sport. In every sport, in every field, the top level people train beyond just practicing their skill.

I'm not saying you have to become a powerlifter and neglect your practice in order to chase 20 more pounds on your squat, but getting up to a decent, base level of strength is a must.