You are quite right that a libertarian king is a contradiction in terms. Libertarianism is not by definition monarchy. Likewise it could never exist under a monarchy. But one of the purely academic problem built into libertarianism is, that if left to itself, it will evolve into a rightwing, highly conservative monarchy. While libertarianism can be accurately described as a leftwing liberal humanest philosophy, the end consequences are clearly the opposite.
There are libertarians in the movement directly and indirectly dealing with this problem, but most libertarians just want to hide their heads in the sand and pretend that their is no problem at all. I am a libertarian, and am anti-monarchist.
if left to itself, [libertarianism] will evolve into a rightwing, highly conservative monarchy Clearly, when libertarians gain power, they will have to set up a politburo tasked to prevent any such ideological slippage.