round robin at the beginning. As it stands, the teams that win their first match have like an 80% chance of advancing. All they have to do is make sure they don't get blown out in the other 2 matches. Similarly, if you get crunched in the first match, it's basically game over.
But if you have 5 teams fighting for 2 spots, it ratchets up the intensity, and everyone has at least 2 or 3 meaningful matches. And for most teams, all 4 matches would probably be meaningful, given that nobody could just coast through if there are only 2 spots for 5 teams.