Why would normal citizens vote for the president? There are only two possible outcomes of that: a president gets selected who basically blocks what the rest of the government wants (this is how it works in the US and exactly what the FF wanted) or the people pick a president who would work with the government but would have been picked with your current system.
The problem is that there is no real choice here; you have a right-wing party and a slightly more right-wing party, and then a bunch of powerless minor parties. Nobody is holding the country ransom because there is no real disagreement. Occasionally the parties clash over the budget (as they did recently), but on the whole the country has generally followed the same path for decades now.
Giving the people what a majority of those people want is a very dangerous thing to do. Part of the theory being having constitutions is to limit the tyranny of the majority, though it is plain to see that in Joe Arpaio's case the limitations are not sufficient. What 51% of voters in Maricopa County apparently want is unacceptable.
They do run in partisan elections, but they are limited with regard to claims they can make about opponents, and a non-partisan commission evaluates the overall qualifications of each judge.
Are there issues with politicalization? Absolutely. But don't make the assumption that election == politics, and appointment != politics. An elected judge at least nominally is accountable to the people. The examples where this system doesn't work well is usually when machine politics corrupt the process of electing judges. If the judge was appointed, chances are they would be accountable to nobody at all.
