I think the personal development and growth from playing multiple sports was immense and yet, I do think kids can experience great growth in themselves from specializing.
I personally believe that my experience in other sports helped me relate and transfer skills from other sports into baseball when I started specializing in baseball. Playing basketball helped me relate and transfer some skills to my defense. Playing football as a safety, RB, and WR helped me track down balls over my head, understand angles on balls, and how rhythm, timing, and anticipation works in athletics. There were many skills in baseball that I didn't have to figure out because I bought them from other sports into the baseball context.
Additionally, playing multiple sports gave me a break from baseball and always got me burning to train and play ball when the spring came around.
I think it's always helpful to know what the end goal is. I want my kids to develop their global athleticism, find something they love, and allow them to discover what they love so they pursue it with all they have.
I wouldn't want my son to specialize too soon and prevent him from potentially discovering a passion for something else because he was never exposed to it.
Up until my sophomore year, I played 3 sports. After sophomore year, I quit basketball because my vision for baseball was to play at the highest level and I wanted to train for baseball during the winter. I still played football but I'm very grateful for the opportunity to discover that desire and passion on my own, as well as be in a position to know that I didn't love basketball the same way I loved baseball.
Because of that exposure, I knew baseball was what I wanted to invest my time, energy, and resources into and gladly woke up early before school to hit in the cage and gladly stayed late after games to hit or train in the gym while others were going home. It was a not a sacrifice at that point but a joyful pursuit.
Again, just my personal experience.
Appreciate everyone's 2 cents on this too as I'm raising a couple youngsters!