Yes everybody agrees they are important in a swing. But I believe these larger muscles are equally important in making the barrel turn specifically, correction, not making, resulting in TTB
Many of the hitters I work with initially have a poor barrel path. So our focus initially is to focus on TTB. Does it fix everything? No. Sometimes we need to work on something else; separation, timing, etc. But the focus on TTB, when done properly, seems to fix some of the other issues as well, so that is where we start. Unfortunately I do not know any cue, catch phrase, or drill that has a 100% success rate. It requires some work on my end to determine what step will help each specific hitter the most. If I could simply walk into a cage, say "turn the barrel", and walk away, life would sure be easy