On the other hand, it's a crowded market that no one has proven is at all lucrative.
There are a lot of F2P games that have been lucrative. Maple Story and League of Legends come to mind as the most obvious. TF2 has also generated more profit since going F2P than it did when it was a retail title.
If there was no proof that F2P could be profitable, nobody would be making F2P games.
Sorry, meant F2P FPS games. Are you sure about TF2? Quake Live didn't generate much, and all of the "pay more for more weapons" games have failed to do much of anything.