I store fruit next to my computer, but the chocolate is in a cupboard downstairs. This is because I know that I'm lazy and greedy but would prefer not to be. I can have chocolate or I can refuse to get up, but if I do one I can't do the other. I'm not sure I could successfully fight my vices alone, so setting them up in opposition to each other seems like the way to go.
I think that problems in games can be set up to oppose each other in similar ways, having one issue act as the solution to another. Let's pick a couple of examples:
Virtual elimination is a problem whereby a player can no longer meaningfully impact the game but is not permitted to leave the game either. For instance I had a game of Game of Thrones this weekend in which one player managed to lose everything but two ships. There's no chance of coming back from such a position, but their ships are enough of a meaningful obstacle to other players that they can't reasonably just be removed from the board. It's a horrible state for a game to reach, because nobody wants to have a player forced to sit in a game that they're not really playing.
Kingmaking is a problem whereby the winning player was not responsible for their own victory. Ultimately the level of skill exhibited by the few players at the top is irrelevant, the decision of who won fell to another player entirely. This is most common in games like Munchkin where the winner is more often decided by who was targeted by 'screw you' mechanics over the merits of a particular player. For a lot of groups this sort of effect is undesirable as winners like to feel responsible for their own victories.
These problems can be made to exist in opposition. A player suffering from a virtual elimination is unlikely to be a kingmaker, as they cannot meaningfully impact the game. A player who's a kingmaker is unable to suffer a virtual elimination since they're still having a highly significant impact. The trick for a game designer would be to find a way to use this opposition to eliminate one of the problems while restructuring the game so that the other isn't a meaningful drawback.
I haven't played a game that does this, but I have heard of one. I'm told that A Study in Emerald uses the following mechanic: Players are in teams, but at the end of the game the team containing the player with the lowest score cannot win. In this way a virtual elimination is prevented, a losing player does not need to recover completely, they only need to reach second to last place to have an impact. The kingmaker scenario still exists, in that a losing player is now having a large impact on the outcome of the game - but as it is enshrined by the rules and something that winning players are expected (and given the tools) to strategise around the victory feels earned.
I look forwards to trying the game at the next monthly meeting and seeing if my thinking about the possible impact of the mechanics is accurate, but either way the notion of setting up flaws to oppose each other and then embracing one to make a better game feels like an interesting idea to play with
Edit (22/07/15) I've now played a Study in Emerald and as mentioned in the comments, it's not what I thought it was. It's interesting to speculate about what sort of game might overcome this duality though, intelligently eliminating defeated players or triggering an end game state sufficiently early to avoid a virtual elimination or kingmaker seem to be the dominant approaches.