How does libertarianism allow billionaires to run the country in a way that liberalism and conservatism doesn't?
Not much time for this, but the problems with the modern formulation of libertarian ideas, is they are separated, corrupted and debased from far better and more reality-oriented libertarian ideas of Adam Smith. In his book
The Theory of Moral Sentiments, Smith argued that humans’ innate sense of empathy and sympathy forms the basis for civilized life. “The man whom we naturally love the most is he who joins to...his own original and selfish feelings, the most exquisite sensibility...and sympathetic feels of others.” The idea of market forces here is producing goods for others as a good for yourself without hurting others. This is as far from the modern right wing libertarianisms, iconic in the idiocy of Ayn Rand, as it could be.
The problem since especially after World War II is that while inflation and costs of living (everything, but monumentally healthcare and higher education) skyrocketed, the ultra wealthy did ever better and better, and as they colluded with some very bad politicians, enforced ever greater benefits for themselves and ever more painful reductions in income and the ability to succeed in society for the middle class and the poor, and in fact developing a system for creating the latter out of the former. Even worse, in the mind-bending, upside down world irony, politicians gain and keep office by giving massive welfare and tax breaks
to corporate power--this is the name of "libertarian" notions but totally opposite to them, and the ideas of Smith.
This is why libertarianism is now dead, in its ability to appeal to voters, because it has been corrupted so thoroughly by the hyper-rich, big corporations, and some politicians who for about sixty years have been so obedient to collude with them. This is no longer about free market forces creating better stuff for the public, and certainly not in line with the government getting out of the way of business, but rather picking winners to permanently keep winning, allowing them to hurt the public as doing so improves profits, in collusion with campaign funding sources from them.
The actual ideas of the long gone Smith libertarian philosophy I am talking about are totally at odds with mindlessly cutting taxes for the hyper rich, using that to reduce service democracy would produce, against rejecting protections of the environment, against attacks on regulations that in fact, actually would
allow for personal freedom and for better competition in market forces, against allowing collusion between corporate power and politicians (to actually crush competition), against insane rates of CEO pay of 1500 times that of their lowest paid workers, against rulings like Citizens United, against the phony meritocratic delusions of the powerful enforcing such increase in wealth and income disparity, and against any dogmatic and unsupported insanity like "trickle down, supply side economics."