A legitimacy crisis is when people stop believing that the governing elite is competent and benevolent.
In theory, a libertarian might welcome a legitimacy crisis. If people lose faith in the government elite, then should that not make them more libertarian?
In practice, we are seeing something closer to the opposite. We are seeing a decline in legitimacy, although it probably does not qualify as a crisis. In any case, the rise of populism helps to promote demagogues, such as Donald Trump and Elizabeth Warren.
Today, libertarians are losing whatever allies we once had. We used to have progressive allies on social issues, such as free speech or regulation of sexual conduct. The younger generation among progressives is opposed to free speech. In the 1960s, college campuses ended their rules concerning visitation of dorm rooms by members of the opposite sex (only a few years before I went to Swarthmore, the rule was that the door had to be open and each student had to have one foot on the floor at all times). Now, the campus sexual rulebook is thicker than ever.
We used to have conservative allies on markets. Now, conservatives are happy to excoriate the tech industry or the pharmaceutical industry or outsourcing. Tyler Cowen’s love letter to Big Business is a rare libertarian voice being drowned out by other voices, such as J.D. Vance or Senator Josh Hawley or Mary Eberstadt.
Perhaps the natural tendency is to oppose liberty. I speak of FOOL, which is the Fear Of Others’ Liberty.
One possibility is that liberty, when it includes liberty for others, is a value held by only some elites. When those elites are weak, FOOL holds sway, and demagogues emerge to satisfy the FOOL.