You don't want to keep score and play for fun, go join a rec league where that's the singular focus. At the high school level and above at the scholastic level, there's nothing wrong with being competitive and keeping score. It's the coach's, AD's, and parent's job to help keep the proper perspective for the players.
The crazy thing about those baseball games where they give out those cards...they still keep the score on the scoreboard! GASP!
And you want those very same people who you allege to not pay attention to the game to start paying attention by making them keep score? And you want the schools to pay for all that extra paper that isn't going to be used...when a lot of schools can't even afford a third official?! What if a fan doesn't have a writting utensil? We gonna provide pencils as well? Sounds like we're given a test rather than letting them watch a d*** game of basketball.
CHS, I can't really believe you're suggesting this seriously.