Personally, I think many ancillary activities can contribute to being better at something . for example, a lot of guys feel yoga is very synergistic with BJJ.
But I also think the proof is in tje pudding. Dancing helped your boxer be a better boxer. We can't say it didn't because he was an excellent boxer. There is evidence.
The converse is when a person declares that something (kata) helps them to fight better, when the assertion that they fight well is still in question.
Said another way, we can see from lyoto machida that kata wasn't the thing that helped him apply his considerable karate skills against other, well trained opponents. In order to bring his karate skill to bear, he added a competitive training model to his karate and also crosstrained in other, complementary styles.
Did kata help or hinder? Who knows . If he says it helps, who am I to say? But I think there is evidence that kata wasn't the difference because the things that did clearly help machida are the same things that produce predictable, reliable, repeatable, and demonstrable results in literally any person who trains in the same way, who do not do kata.
Edit to add an analogy, just because.

If I weigh 400 lbs when you see me and then 2 years later I weight 185 lbs, you might say, "hey man. Congrats! How'd you do it?" I could say, "dude, I owe it all to meditation. 100%. Oh, I also started eating clean and training BJJ." Was it really the meditation? Maybe that helped me stay committed to training and eating healthy but the diet and exercise probably had a more direct influence on the weight loss.