Rules question: can president nominate him/herself to be Chancellor?
If the president wasn't part of the last government, and didn't enact the last policy, then presumably the president can nominate him/herself for the role of chancellor. No guarantee s/he will win the ensuing vote (may likely lose since people would likely be reluctant to give someone so much power) but it seems like it should be legal.
It may present an interesting situation, one where the same person gets to choose without anyone else stopping them whatever policy they want. Of course this very thing may be legal but it would be foolish for people to do this unless they knew for sure they would be benefit.
Lots of interesting situations occur if people utilize this strategy given when in the game it occurs.
Another way to express what you are suggesting is that a player draws three policys and chooses one to enact. This could be a perfectly good variant special power (In the 5-6 player game it may be a good substitute for the 'Peek' ability), but it's not part of the official game.