As for Paleo, the belief that humans weren't eating starches way back when has been debunked:
The Paleo Diet Is Uncivilized (And Unhealthy and Untrue)
The belief that the Inuit Eskimos are a healthier people is not true either:
"evidence has shown that Inuit have a similar prevalence of coronary artery disease as non-Inuit populations and they have excessive mortality due to cerebrovascular strokes."
Paleo was even recently rated the worst diet:
Paleo rated WORST diet! Low-fat rated high (U.S. News)
About a vegan diet, there's lots of ways to eat a vegan diet, but for those here at this forum who got sick on a vegan diet, all of them were under-eating at the time:
All who got sick when Vegan under-ate
This is also what happened to Paleo-Queen, Denise Minger:
Ex-raw vegan under-ate, but blames diet
But regardless to all that evidence, the biggest evidence that I base my belief that the Paleo and other low-carb diets are unhealthy is not only what happened to me from years on those diets, but from observing the diet habits of people at this forum who are still sick:
Just like with every other popular protocol pushed at this forum, Paleo seems to have a very low success rate. All you have to do is go to the Candida support section where just about everyone there is on the "Candida diet", which is basically the Paleo diet, and hardly any of them are getting better.