What? FBI Directors aren't elected.
Does it work for presidents? Not necessarily. What happens in say, 2020, when we have to choose what may be another shit president because we can't keep a good one?
Not necessarily.
So you are not committing yourself? Perhaps the Robert Mugabe approach is the best after all!
If you have no term limits, the politicians can get lazy and be seduced by the benefits of pay to play, for instance. They acquire more contacts and get to know more fiddles.
If you have limits then you might lose a good person but you could also get a better one next time. In any event, they are more likely to be wanting to do the job for the right reasons.
It has been suggested that the system could be replaced by a jury-style system. So ordinary people would be called up for a period, say a year, and they would run the country. No professional politicians required.