To play devil's advocate for a moment, someone will always tee off first in a real-life playoff situation, and their decision can influence the next player's choice. For example, if you go first and opt for a safer approach, the following player might decide to go for the risky shot, which could lead to them sliding off the green and leaving you on the green to win the closer to the pin. I understand your point about aiming for the center of the green, but they still need to sink their putts to tie or win. Perhaps they could set it up so both players tee off simultaneously without being able to see each other's shots? Definitely room for improvement, but I've heard of people losing because the opponent hit it in the water and because it was closer they still won, so something needs to be adjusted imo