No, the problem is that we don't have an electoral system that makes it rational to choose such a candidate without reasonable basis to believe lots of other people will (choose the same candidate, not just any non-major-party candidate).
The symptom of that problem is that nearly no one chooses an alternative candidate.
More concretely, the Paul family might one or two things I agree with, but it's the other 999 things they believe in that I can't stand, thus I can't vote for them so much as against them.
I'm not just talking about the presidency... or am I missing something?
Neither am I. In fact, I'm mostly talking about legislative elections, where the use of the first-past-the-post elections in single-member districts produces both duopoly and about as unrepresentative of a legislature as you can get in a system which is even superficially democratically accountable.
People like to focus on the electoral college, but that's not really the main problem in the electoral system in the US.