There's no point in arguing the point to death, but it's only the voter who fits the 50-50 profile of such a political party perfectly who would be likely to join.
Except "only the voter who fits the 50-50 profile of such a political party" constitutes a large portion of the population, as was demonstrated. The problem the American Solidarity Party faces right now, and hopefully will be changed over time, is that it's not very well-known (which makes some sense given how new it is) so it isn't able to really tap into that portion of the population at present.
Meanwhile, it leaves the party itself to have to explain what matters on the conservative end of things, and what matters on the liberal side of things, and also what is consistent about that. (?)
"Socially conservative, fiscally liberal." Not exactly a difficult explanation. Granted, that
is an oversimplification, but it does describe about 90-95% of its positions pretty well.
Well, the Libertarian Party IS sorta conservative and sorta liberal, if truth be told. And it's been around now for almost 50 years and usually gets 2 or 3% in national elections. So I wouldn't call that a smashing success.
Compared to every other third party since the Reform Party, the Libertarian Party
is a smashing success. And even the Reform Party wasn't really a party so much as a vehicle for Ross Perot, and ceased relevance about as soon as he did. So the most successful third party, by a notable margin, is the one that is "sorta conservative and sorta liberal". The Green Party and Constitution Party, in contrast, are pretty thoroughly liberal and thoroughly conservative, and don't do anywhere near as well.
However, the Libertarian Party faces an issue that the American Solidarity Party doesn't: A relatively low ceiling of support. Look back at that chart I posted. The lower-right quadrant, which is where the Libertarian Party, is by far the least-occupied quadrant. So while the Libertarian Party serves that quadrant (which is not served by Democrats or Republicans), the low population of it is a major part of what keeps the Libertarian Party small.