I'm sure the showdowns were designed to engage the mobile players, which is why the coin format is used and coin games are more or less a form of match play with the added element of a little bit of betting. It's always seemed odd that stroke play scoring takes precedence over the matchup.
Match play scoring could add a bit of drama to the early rounds if better players couldn't just coast in knowing they're above the cutline, and had to take some chances to win matches to advance.
However, it wouldn't solve the problem of mismatches between higher and lower tier players leading to forfeits and cheap wins skewing the results. I had a match against a level 18 Hack that I would have gladly forfeited in the last round, but couldn't for sake of the score.