American "libertarianism" is anarchism (aka libertarian socialism, or just libertarianism) twisted through the sick lens of syncophantic hyper-capitalism. What do you think will happen if government limits on capitalists disappears and corporations are free to do what they want? "Freedom?" Or SciFi dystopian corporatocracy -- "In the name of OPC corp, drop your weapon, you have 20 seconds to comply!"
Americans, having been brainwashed by the mythological rugged "free" individual becoming rich as a Rockerfeller (despite research to the contrary; people generally stay within their socioeconomic class; Bill Gates was born rich enough to to afford to drop out of Harvard, his Dad is a high powered lawyer, his Mom served on the board of the directors of a bank).
Understandably turned off by the two elite parties, and having been brainwashed to see everything in their own class interests (such as universal health care, housing, education -- spending all the taxpayer's money on killing the non-white people du jour are A-OK, though) are evil commie-ism, not to mention the "rugged individual" mythology, they see the fringe Libertarian Party, favourite of naive white males and rednecks, as a viable option.
What a sad state of affairs that some people see the LP as anything other than a dead end. Just be sure that if the Libertarian Party ever came into power, it would just be reproducing the current state of affairs -- elite rule -- but much more extreme without even the minimal protections for people of the interests of business.