I didn't say coaches call the pitches today. I know they don't. I'm looking at it from a problem-solution standpoint. The problem is: pitchers and catchers need to synched up, with regard to pitch type and location, without the batter finding out. There are many possible solutions. One way is to have the catcher call the pitches and use arcane sign language to communicate it to the pitcher. Another way is to have a third person suggest pitches to both the pitcher and catcher, getting a simple nod in approval. Both have downsides. I'm sure if we brainstormed, we could come up with a dozen more ways to solve this problem, and I'm sure most would be better than the the silly hand signals. I thought they were dumb when I played as a kid, and I think they're still dumb.
In terms of game speed - I agree about the commercial breaks. However, there is no changing that. You said MLB is more profitable than ever: this is why. Viewership is down, but profits are up. It means they're milking the remaining fans for more.
If I had a magic baseband wand, I would make a rule prohibiting coaches or the catcher from visit the mound mid-batter. Once the first pitch to a batter is thrown - no more interruptions until that batter is out or on base. I would also enforce the batter's box rule. I'm not a fan of the pitch clock idea yet, but it should be tested in some lower leagues.
With regard to tradition, a mentor I respect a lot told me: If tradition or "this is the way we've always done it" is the leading reason someone gives for resisting a change, then that change is certainly needed. The context was process, but I think it applies broadly.