If Plato and Aristotle anticipated today's Neoreactionaries, well, you can't exactly call Neoreaction an unhistorical, ungrounded, fringe view, can you?

I'm not sure what "unhistorical" is supposed to mean, here, but you can definitely call it ungrounded and fringe. Fringe is obvious; look around at political philosophers of all stripes, and find as many Neoreactionaries as you can; it will be at most a tiny fraction of the population. Which is exactly what is meant by 'fringe view'.

In terms of claiming ancient views as demonstrating solid grounding for a belief: people long ago believed many things which we know now to be wrong and baseless (given adequate data). Plato and Aristotle themselves inherited from predecessors like Zeno, Thales, and Anaximenes, who all believed things we now know are indisputably wrong. (The paradoxes of impossibility of motion, everything being composed of forms of water, and everything being composed of air, respectively.)

The grounds that Plato and Aristotle had to believe those positions were that their society looked approximately like that, and, to their (probably biased) eyes, looked like it was doing much better than anyone else around. If we look around now, we don't see any society that has that form, and those historical societies that did didn't do well in the long term. The grounding has been lost, and claiming 'this used to be well-grounded' as grounding now doesn't obtain.