Let's play this out.
Team A scores 150. Team B scores 175. Team C scores 100. B beats C.
A = 150 vs. (B175 + C100)/2 = 137.5.
Are we really going to declare Team A the winner when Team B scored 175 points?
Maybe. Would it be better to do 2/3 instead of half? 3/4? I mean there is basically a 50-50 chance that Team A should have played Team C who scored 100 pts. As long as the rule is known ahead of time it's fair. The whole system is random on who scores anyway.
I still think the "fairest" outcome where 3 teams still have a chance to win something is to have 2 games on the final weekend: A vs. B and A vs C. Winner of Game 1 gets 50% of first place money. Loser of Game 1 gets 50% of second place money. Winner of Game 2 gets 50% of first place money. Loser of Game 2 gets 50% of second place money.
Possible outcomes . . .
Team A goes 2-0, gets 100% of first place money
Team A goes 1-1, gets 50% of first place money and 50% of second place money
Team A goes 0-2, gets 100% of second place money
Team B or Team C go 1-0, each gets 50% of first place money
Team B or Team C go 0-1, each gets 50% of second place money
I get that Team A could gripe about having to play 2 games, but by going 1-1, that's a better payday than only playing 1 game and losing outright. It also makes for a weird outcome if Team A loses both games, as there technically wouldn't be a league champion.