The main issue with doing it this way is we don't really gather anything useful from votes this round. The positive is that there is a 1/5 chance to kill an mafia member and only a 1/10 chance to kill a seer/doctor. That is, if everyone votes. Of course, that is somewhat true regardless during the first round, but this way you don't have a team of FG's that can influence who dies.
Also, we probably shouldn't assume that FG's won't vote for each other this round since a voting pattern has already been established.
Also, if EVERY round is done this way, completely at random, rounds should go like this, more or less...
R1 - 18 alive total, 4 mafia alive
R2 - 16 alive, 4 mafia
R3 - 14 alive, 3 mafia
R4 - 12 alive, 3 mafia
R5 - 10 alive, 2 mafia
etc.
And if we got lucky and the seer lived during this time or the doctor saved someone, we'd likely win. If someone wants to do the actual math about how often an FG would be killed at random, might be nice... I just took an educated guess. On average, the ratio should stay the same throughout the game at 1/5 players mafia at any given point, and having a seer/dotor SHOULD give the civilian side a mathematical advantage, I would think.
Edit: And good point, Terro, I missed that. And I didn't take voting manipulation into account for this... might mess up the numbers.