I do think it would be best changed to a 0/2/4/5, rather than the current 0/1/3/5.
This change buffs narrow victories and tie games, also known as CLOSE games, which are more intense to watch anyway, and are the reason that the time limit exists at all.
Also, it results in more things that make sense.
See, in the current system, if you sum the total scores of the two players, you can get a 5, a 3, or a 2 (for a tie).
In my system, it's a 5 or a 4 (or a 4 in a tie), making it far closer to a zero-sum game (which is better for keeping score in a tournament).
Similarly, apply my version to the scenario in the Original Post, or apply it to the following microcosm instead:
Two players are evenly matched, and fight twice, resulting in one of the two following options:
Player A squeaks a victory by Player B in the first game, and loses just as narrowly in the second, as it came down to dice
OR
Players A and B tie both games, as there was less variance.
My system? A and B are both sitting at 4 points, regardless of the scenario, and have similar standing to all other 1/2 win/loss ratio games in the tourney, and can still compete for the final four.
Their system? A and B are sitting at 2 points if scenario B, or 3 points at scenario A. Moreover, neither score is good enough to ever have a shot at top 4 vs opponents who scored a full 5 point victory with a loss.
It's such a simple fix. How does the game break if it were implemented instead of the current ruling (which has its own issues?)