I'd say where my sons HS coach played a role, was recognizing my sons talent and giving him a chance. He started his freshman year, and in the CCS games, he started 2 out of the 4 games. In the final game he was recognized as the top hitter. There were several college scouts there to see many of the upperclassmen, and as it turned out, his travel coach got phone calls after the game wanting to know about my son.
So, we were in the same situation as others posted, HS Coach was not a factor in recruiting, as he had limited contacts. Travel coach had many contacts, and also helped navigate which schools over recruited or were 8-10 deep with players in my sons position. It was nice to see a Power 5 interested, but would he play? Travel coach was instrumental guiding us to schools that were interested and knew what positions the coaches "needed" to fill.
Also, Head First and Showball were not just academic showcases. They're expensive, but not just for the high academic player. As it turned out, Showball was where my son got noticed and followed by several schools.
A very good write up, though, with excellent points for parents and players.