I was a multi-sport guy as were all of my kids. The HS where I coach (and where they attended) is still just small enough that many student athletes can choose multiple sports and make rosters. When I observe players that come into (or out for) the baseball program, it's a mixed bag. For some, they really should also play other sports for a variety of reasons. For some, the only way they are going to crack the lineup is to play a heck of a lot more baseball outside of the HS season and get additional instruction/reps. This really has nothing to do with adults in the room. It's just the fact of the matter as to where they stand in the current competitive environment they are trying to navigate.
I'm torn on this issue. I would love high school age kids to play multiple sports if they want to. But, when they play sports, the majority want to be competitive (it's not just the coaches and parents) and that IS, after all, the object of sport - to win the game. It is my experience that for the majority, those who play more games and get more good instruction will have more advanced skill sets and game awareness particularly at the mid-youth and HS levels. This becomes a difference maker in competing at those ages. So, in the end, the HS starting lineups are typically loaded with those who focus primarily on one sport. The exceptions are those who are well above average in athleticism and those who are at smaller, less competitive schools. Again, I don't really see this as an "adults screw everything up" issue. Adults are involved but they sorta have to be, don't they?
I totally agree that kids should play a variety of sports when they are very young, just as they should be introduced to a variety of other things. But at some point, interests and competitive environment will begin to narrow their selections. That is not to say they cannot still enjoy other sports on a more recreational level.
I, too, could tell endless stories that could support either side. Most recently, I have a player who was our best offensive producer as well as a defensive standout at the V level the year before last. He had decided prior to put all of his efforts toward baseball. Then, this year, he decided to pick up soccer again. He came out from soccer to baseball, having missed much of the preparation time he enjoyed the previous year. He struggled quite a bit, particularly offensively, because he just wasn't as sharp and prepared as he was the year prior.
On the other side - same two seasons - there is a player on JV who was quite weak and un-athletic but had decent mechanics. He was not on the radar to advance to V at any point. He decided to play football the next fall. The improvement in strength and athleticism was pretty remarkable. He was now on the radar.