As Erasmus said previously it has been done. But don't let that stop you if you would like to run a competition. A lot of competitions get a reasonable number of players who participate in tournaments simply to have fun knowing full well they probably won't win the cash reward (if there is one).
Currently a BSG and PD Proleague style of tournament is being held... the BSG/PD State of Origin. To the best of my knowledge there's no prize for that... but I can assure you there is a lot of state pride! This is proof that it's not too much for one person to organise (although many hands make light work) and the willingness of people to join "priceless" tournaments.
Also, for reference: The match type you described which sends players to a lower bracket is called "Double Elimination".
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