The points that I am making will become painfully clear this Sunday if we have a randomly seeded single-elim tourney. Some brackets will be much harder than others. Those brackets will have long and difficult games that will fatigue the winners, while other brackets will give an isolated top player an easy route through. The players in easy brackets will have a strong advantage in the later rounds playing against players that have struggled through the difficult brackets. You don't need to do a bunch of math to figure out the chance of this happening. It simply will happen, and you'll see what I mean this Sunday.
I'll immediately be able to tell you the tough brackets compared to the easy ones and show you how that is not fair to the players that got stuck in the tough brackets. If there are only 4 tourneys per month before the reset, then the effect will happen over and over again. Arguing in favor of a randomly seeded single-elim just boggles my mind.
If you want fairness and no seeding, then run Swiss or at least double-elim, where the tournament format itself accounts for the lack of seeds, and ensures that the best players fight one another at the end of the day.
Oh please, Ami. If you cared about players "fatigue" or their "easy route," you wouldn't do things like invite players to skip an entire qualifier weekend and go straight to main event in OCF (where they have to just win just a few games to earn some money). This style hardly seems fair to me. And as we saw with Jesulin (whose performance isn't what it once was), these invited players are not guaranteed to make it to the finals.
I get that you want spectacular matches in the later stages of the tournament to feel like the stakes are high and uncertain who will win, but you will usually get this even with random seeding (I know this from personal experience in DOW2 tournaments). In fact, it was hardly the case a low level player would make it as far as the quarter-finals given the amount of high level players vying for the win.
On the flip side, yes sometimes some people, including me, got paired up with some heavy hitters early on in the tournament; but like Yukiko said, these instances are rarer than the general trend of an even spread.
Both formats have their merits and downsides. I wouldn't call seeding of tournaments the superior format.