We tried a World cup one once, that was based on the "one player" per team thing.
The bidding stage was incredible fun. Blind bids, and that excitement to see who'd you got. Laughing at those who'd bid insane fees for certain players, and those who'd ended up with 80m spare after all the good players had gone!
The big problem, was that after the bidding, the fun dropped off massively, and you were totally locked to what you had. No freedom. I suppose that'd be the problem with the rule you mention, or any single player rules.