I never see anyone playing this way, but I’m pretty sure it makes perfect sense. After you go eye-to-eye to determine first shooters, the team that LOSES should shoot 1st, but only with 1 ball. Then the winning team comes back with two balls.
This is superior because the team that won still gets an advantage (imagine a perfect game thrown by both teams, the 2nd team will win) but not as big an advantage as starting off with a 2 ball headstart.
It’s not as big a deal in 10 cup games, but whoever starts with both balls is at too big of an advantage in 6 cup games.
That’s how I learned the game, and that is how we will most likely play at The WSOBP (simply because of what you just pointed out). To determine who gets the first shot, however, it will probably be determined randomly.