I think a better critique is that these cold-war political basis vectors don't adequately describe today's political landscape (and neither do the revolution-era idea of the left wing vs the right wing; arguably they didn't back in 1950 either).
Best example of how the communist/fascist/liberal democracy triad completely falls is looking at China, which has facets of all three and none at the same time.
This makes it difficult nigh on impossible to have a real political discussion, as they fail to amount to more than connotative terms to be applied to outgroups, and do not map to political reality in any meaningful sense. Anyone can turn into the fuzzy outline of a nazi if you squint really hard.
Nuances needed to make any sort of sense of 21st century politics, especially its newer entries, are the tensions between cosmopolitarianism vs communitarianism and technocracy vs populism.
The problem with using such an outdated political map is that many of our contemporary problems are missing from it, and go unresolved until enough frustration builds that there is an ill-conceived popular upheaval that forces the issue. Rather than addressing the technocratic European Union's lack of accountability to its citizens, we get Brexit instead, which could likely have been avoided if the political map wasn't so out of touch.