There's obviously a lot of overlap between Paleo and LCHF; it's a sliding scale of carbs from virtually nil (<50g a day) for the Nutritional Ketosis promoted by Phinney & Volek et al (and indirectly, Atkins Induction), to a lowish level (100-150g a day) for the likes of Mark Sissons (Paleo Blueprint).
I originally came at this from the extreme low-carb end. After a brief attempt to get back into keto ways after the end of the audax season, my diet has become a disaster zone - victim of a seasonal visit from The Black Dog (Chocolate anyone? No? How about a couple of packets of Chocolate Hobnobs? You can wash it down with this nice bottle of red... you get the idea). I quite like the idea that eating real food panders to our gene expression, but nobody really knows what we used to eat, back in the day. Probably stuff I'd never dream of eating; organs of kill, insects, roots, berries. I'll do berries, and roots if they're potatoes or carrots. Oh and lets not forget, we're actually really good at going without. Sure - we'll be hungry and miserable but nobody said it was our god-given right to be happy all the time.
I think it's a very reasonable thing to say "Our diet has to be good enough to get us to breeding age, and no better." And in that, we are pretty adaptable. We can eat pretty much anything it would seem, and subsist in some way. We're really really good at putting on fat when carbohydrates are in abundance (don't I know it) and can live off that really effectively for bloody ages, which is why it's so damn hard to lose the fat again.
But surely the modern take on this is not just to get to breeding age, bang out a few rug-rats and then peg it? We're looking for a diet/way of life that can (a) co-exist with our modern "busy" lives, and (b) allow us (within the limitations of our genes, damn them) to live as long and healthful life as possible. Do I think Ancel Keys had it right? Hell no - and I think that's where Paleo and other low/moderate carb diets will lead us. I can't decide if I want to succumb to the whole conspiracy theory that we're all victims of a HUGE crime perpetrated on us by Big Food and Big Pharma, ever since Lyndon B Johnson bowed to his farming buddies and backed Ancel Keys' completely bogus "Seven Countries" study that (wrongly, because he left out most of the data that disproved what he was wanting to prove) apparently linked cholesterol with heart disease, and that saturated fat was to blame, thereby opening the doors for forty years of Sugar and Wheat based dominion over us serfs. I'm not quite that paranoid. But then again, I have learned that if I want to lose body fat, cutting carbs, not calories, is what works.