TL;DR Version
I think the site should require that all games using First-Come-First-Served power selection should also require a password.
Background
Diplomacy's powers aren't balanced, and that's OK. Over the course of a lot of games, with a lot of different players, there are identifiable statistical correlations between the powers and their results. It's the truth for almost any variant of Diplomacy too.
This in itself is not a problem. The asymmetric setup is part of the character of the game, and experienced players can use a power's relative strength or weakness to inform their negotiating tactics.
The Issue
What I do see as a potential issue is making it too easy for someone to play only the powers they want to, particularly if those powers are always the strong ones. This would be particularly true for variants with much larger power disparities than classic Dip. Currently, this is easy to do: you can post a game, take your favorite power, and hope others will take the remaining slots.
This just strikes me as somewhat outside the spirit of the game, like a pool shark waiting for unwitting prey.
Impact
It's more of a theoretical problem at the moment. At the time of this posting, no open new games listed up with FCFS are Rated games. There are 15 that are Unrated, which is still a teensy bit concerning (since even though unrated games have impact on personal ratings, they're still ostensibly supposed to be fair games).
Caveat
Occasionally, people will organize tournaments, league games, and other events where power selection is done externally, and those players are instructed to select their assigned power when joining the game via the site interface (with mods called to boot non-compliant players). These games may be rated or unrated, but they tend to be password-protected. This is a legitimate use case for FCFS.
Proposed Solution
We should require that any game set up as First-Come-First-Serve should also require a password. This way, they're less likely to show up in a typical search result, and it becomes harder to lure random players to the "I already picked the best power now come play with me!" scenario. But it also doesn't get rid of the functionality completely, and players that want to recruit for a game via the forums with specific power assignments can do so.