FIRST $CASH$ prize...

[Lil' Lavery]

No cash/refund/etc. should ever be given to a Champion of an official FIRST event. Period.
As for Scholarships, there are already a multitude available, including one that essentially is a prize. The winners of the Championship Chairman's Award select one student for the Allaire Medal:

5.21.5 The Allaire Medal - Leadership Exemplified
The Chairman’s Award is presented at the Championship to the FIRST team judged to have the
best partnership effort. The Allaire Medal recognizes leadership exemplified and is awarded to
an individual student on the winning Chairman’s Award team.
Named in honor of Paul A. Allaire, a long-serving FIRST Chairman of the Board, the Allaire
Medal is given to the student who has demonstrated outstanding leadership on his/her FIRST
team, within his/her school and community, and whose personal character best embodies the
spirit of FIRST.
The team receiving The Chairman’s Award at the Championship will select the Allaire Medal
recipient. The adult and student team members determine the winner. The recipient must be a
high school junior or senior who has been accepted into a four-year degree program at a college
or university. The Allaire Medalist receives the Allaire medallion and up to $10,000 in total
scholarship support for undergraduate tuition, room and board, fees, and books at his or her
intended university or college.

If $10,000 isn't enough motivation for the students to strive to fulfill and spread the meaning of FIRST and the Chairman's Award, I don't know what is.