OK, I just have the party platform to go by… and there’s a lot that seems problematic.

You might be confusing libertarianism and libertarians with Libertarians. Not all libertarians believe everything in the Libertarian platform and vice versa. The Libertarian Party is one manifestation of libertarian beliefs but it is by no means the definitive line of thought.

The party tends to attract a bunch of kooks who don’t want to make as many compromises as libertarians within the Republican or Democratic parties do. Most reasonable libertarians accept and work within the two party system.

On a more philosophical bent, there’s a reason why most populist movements fail. Because a large group of indigent people who are known for poor decision making tend to fail against a substantial group of people with lots of resources and good decision making.

There’s a whole other discussion about fairness, perceptions of fairness, and how people come to either accept or reject the political systems that they live in, but that’s way outside the bounds of this general introduction of libertarianism.