In the game, the act of collecting coins represents raising funds for research into rare diseases. I'm sure it does say this in the start menu but perhaps it could be clearer possibly when the game is over. I considered setting a quantity of coins to reach to cure specific diseases. However, I ultimately decided against it because I was concerned that it might inadvertently imply something inaccurate so kept it the way it is.
I really like your idea about toggling, I'm not sure why I didn't think about that because normally games do make player two press a button to join in. In a future update or if I make the sequel I will make it so player two can join and if any player has not moved / is in the starting animation they will be invincible so then you can aim to beat your last score and not just your best.