Third parties don't work in our current system. If we had preferential voting like Australia, then yes, it would work out that you could vote your party of choice, and give your preferences to the party kind of close.
But sadly, we don't. And sadly, when people vote 3rd party, the main parties ignore that vote. Instead they would rather poach votes from the other main party, and adjust their policies accordingly.
The Libertarians have been running presidential candidates for how many years? And to what effect?
And another thing. Third parties can be pure in their ideology because they aren't in power. If they were to get into office, they find they don't have absolute power to rule by decree. They have to somehow do that messy bit of compromise and dealing to get anything done, because a good part of the people don't necessarily agree with that ideology.
Which is typical of a large group of people.