A player who has his sights set on college level ball should, yes, play competitive ball and that usually means playing on "elite" or high level teams. You only get better by facing good players. That means constantly developing your skills. Playing parks & rec/Little league usually doesn't cut it.
However, by HS age the emphasis needs to go from winning tournaments to showcasing the player's skill set to college coaches. That means participating in PG type showcases. Winning high level tournaments mean nothing if the right people don't see you.
I really wouldn't worry about showcasing until HS age (sophomore-junior year) after the player has transitioned to the 90' diamond. You'd be surprised how many drop out at that point. All of a sudden the 225' HR is now just a long out.
Yes, my son did play travel beginning at 9-10 years of age, but it was more a local travel team and the coach was very selective of what tournaments the team participated in. I couldn't see paying thousands per year when he was at the age. The objective of that team was preparing the players for HS level ball.
And grades are just as important. You can be a 5 tool player, but if the GPA is low it's highly doubtful a D1/D2 scholarship will be offered. NCAA minimum is 2.0 (the school can have a higher minimum) and I would advise an athlete maintain at least a 3.0 (the higher the better). Coaches figure a student's GPA will drop by 0.5-1.0 once they are in college (assuming they get an offer).