Scholarships are a pipe dream, yes they are out there, but for any given kid, the chances are very, very slim. If your kid is good enough to qualify, then I don't think a year either way is going to make a difference.

Have a friend who's son was recruited as a sophomore from a top club to a D1 school (winner of multiple national championships) - and he only got a partial scholarship.

Take all your club fees, private lesson and clinic fees, along with the money spent for gas, food, and hotels, for all of those tournaments over the 6-8 years that you do this, put that money in and index fund, there's your scholarship.