Free contests and the ones I am suggesting are a world apart. Most free contests are longer length and generally do reward skill somewhat. A short, but cheap contest would be much more luck dependent and for that reason would attract sharps and squares alike. Not to mention it is a quick, short time committment thing. You don't have to go for a month or longer to get a winner, most people will be eliminated as soon as they lose a couple games on the board. If the tournaments get some following it won't be that big a deal though, there can always be another one starting.
Besides I think that contests on here or any site aren't the best promotional tools. They don't necessarily create regular viewing of the site by accountholders. That is what would be the best part of it for any book that ran it. You would know that you had live customers in them and you could even make a little profit off of offering them instead of taking your chances with someone that has no intention of every depositing money of their own.