A core value of libertarianism is freedom from coercion. Political parties are the sorts of entities who exert coercive forces on people, so it is a nearly impossible task to organize a libertarian political party. My guess is libertarians will always vote for the least worst option facing them, at a particular time and place.
Your observation that both the right and the left are calling for more government intervention seems correct. The disenfranchised on both sides of the political spectrum feel that something needs to be done, and populists take advantage of that energy to seize power.
Classical liberals, now called libertarians, warned that the preconditions for this sort of collectivist power encroachment were being put in place with the adoption of Keynesian economics, in the 1940’s. I’m thinking of F.A. Hayek’s “Road to Serfdom”, in particular. So prophetic.