You probably have a number of factors going on. It is surprising difficult to find any solid studies however (I'll try to find some later).
Mostly answering wrt the US Libertarian position, since I don't know if too many other countries have a significant explicit party in this domain.
Parents should have control of and responsibility for all funds expended for their children’s education.
Retirement planning is the responsibility of the individual, not the government. Libertarians would phase out the current government-sponsored Social Security system and transition to a private voluntary system.
To further that end, we call for the repeal of the income tax, the abolishment of the Internal Revenue Service and all federal programs and services not required under the U.S. Constitution.
Therefore, we favor the repeal of all laws creating “crimes” without victims, such as gambling, the use of drugs for medicinal or recreational purposes, and consensual transactions involving sexual services.
We oppose the administration of the death penalty by the state.
It's not hard to see how some of these are not going to be very appealing across the US ideological landscape (the last 2 are going to be unpopular with religious conservatives). Reform of pensions for example is a political live-wire everyone avoids.
However, as an influence on politics in general, especially in the US, small-l libertarians, advocating for a smaller state, do have some influence within the Republican party. And, really, cutting red tape, axing corporate subsidies and promoting individual liberties are views that are fairly popular in general. Balancing budgets may not be all that popular, but there are intergenerational equity risks with running near-constant deficits. In short, applying a watered down version of libertarianism when deciding on laws, regulations and policies can be viewed as helpful, by some.
Which is, to some extent, not that dissimilar how Green parties struggle to get elected on their own ticket, but manage to get quite a few of their principles adopted by mainstream parties.
Pure big L-ibertarianism on other hand is unpopular because it is a reductio ad absurdum position with obvious shortcomings in its practical application and ethics.