The question must be...what kind of musician shall we elect ?
In rock and Roll we have very much dope/party and groupies...shall they act as advisers?
In Rap they might talk to fast for a foreigner to understand, so wars might arise even before last tone ended.
Country, well..they always look back and think that was the best time....maybe our Country would stagnate.
Classic...well it must be classic...here you find it all...the heat...the cold...the passion...everything that makes it live....the biggest back draw is that most people don't listen to it, and then would not know the musician when (S)he tried to run for President.
I think the biggest back draw with any politician is that (s)he is a human, and as such has the ability for greed, and the hunger for power.
I am 120% sure that any musician you will bring forward has the same treats, and if they get the opportunity to have power, then keeping it will be the main thing for them, as long as they are able to stay with it.
There is very few that have the strength to see the good of the people first, and to put their own interest last, or even back as second.
You will notice it again, and again...especially where you have "freedoms fighters" that start as a movement to tumble down a despot of their Country, as soon as they have won, they build up a protection ring around themselves, and often become as cruel or worse then their predecessor.
We will always have the danger for such development, even in " the rich world", and it is one of the reasons for wars.
So let us rather make a new law; "those who rule a country, is those who must go in the front line, next time they want a war .....and then musician would be a very good choice:) (just kidding in the last line

)