Let me briefly describe my reasoning for the current setup. I think we can all agree that winning from the first seat is easier, on average. So we can use the "break" idea from tennis, where winning games off of the other person's serve is necessary to win a set or a match.
So there are a number of different permutations that can happen. I'll use players A and B, with A always leading after the fifth game. Here are the various possibilities:
12211 12121 12112 12112 11212 11122
A WWLLW A WLWLW A WLLWW A LWWLW A LWLWW A LLWWW
B LLWWL B LWLWL B LWWLL B WLLWL B WLWLL B WWLLL
21122 21212 21221 21221 22121 22211
22211 22121 22112 21221 21212 21122
A WWLLW A WLWLW A WLLWW A LWWLW A LWLWW A LLWWW
B LLWWL B LWLWL B LWWLL B WLLWL B WLWLL B WWLLL
11122 11212 11221 12112 12121 12211
In the top row are all the possibilities where Player A went first in the first game, and player A is leading 3-2. In all of these groups, the number of games won from seat 2 is equal for both players; each has "broken service" the same number of times.
In the bottom row are all the possibilities where Player A went second in the first game, and player A is leading 3-2. In all of these groups, Player A has one more win from seat 2 than player B does.
In the top row, in other words, there is evidence that both players are of equal strength from the second seat; in the bottom row, there is evidence that Player A is stronger from that seat than Player B. But the only difference in the two rows is whether Player A went first or second in the first game. Therefore:
In the bottom row, the leading player went second in the first game, and has won the match. In the top row, the leading player went first in the first game, but hasn't won the match due to not showing that he can break more often than Player B.