Adds unneeded complexity for players, tourney mods, and hosts, discourages applications (on the grounds that you may want to enter a different one more) therefore reducing tournament size and overall activity, makes it harder for active tournament players to get into tournaments even though many of them are exactly the people we want in.
I think that something needs to change about tournament applications, but this is not the answer. If we find that many people are missing out on getting into a specific tournament, then make that tournament bigger. Encourage hosts to use slightly unusual player numbers to make tournament size more flexible (96 and 48 are actually great numbers, just play it normally down to 3 players and have a three way face off). Force people running tournaments to keep sign ups open longer. If repeatedly there are 64 player tournaments that are oversubscribed, open tournament applications and let a more tournaments in.
Unlike with mafia (which this system is based off) you can easily expand the number of players in a tournament with almost no effort on the host's part. You can also make new tournaments to spread the players more thinly very much easier than you can make new mafia games, if you think that tournament size is getting over the top.
Maybe the biggest problem with this would be that certain players are likely to think "if I enter tourney x, then I may not get into tourney y", and so not enter tourney x at all. In most cases this will give an extra space for another player, however sometimes it will bring the tournament down a size level, and make less places available. As an example lets say 10 players decide against joining tourney x because they want to get into y, and tourney x ends up with 55 people (not enough for 64) so the host cuts it down to a 32 player tournament, there will actually be 23 more people who sign up and miss out, and over 32 who actually wanted to play who won't.
Edit: As for the "this helps newer players" argument, as it stands newer players are on a even footing with the best. Right now the EWs and Goukis have the same chance of getting into a normal tournament as everyone else, except maybe they check this forum more often. This would actively discriminate against top notch tournament players who enter as many tournaments as they can.
tl;dr: Not a good way to approach the problems, won't help much, makes extra work, puts people off joining tournaments, a not insignificant portion of the time will lead to more players missing out. Lets not.