To give some further analysis which I didn't cover in this video, I think theoretically if you live a lightly active or sedentary lifestyle then a low carb diet is a viable option. Our body can convert other substrates like fat and protein into glucose in the liver via gluconeogenesis to ensure we have at least minimal glucose and glyocgen stores in our body for basal metabolism.
When we break down glycogen it forms a byproduct, pyruvate which can be recycled back into ATP through the kreb cycle. Problem is, you need oxygen to do that so if you're exercising above the lactate threshold (the point which you can no longer use oxygen, anaerobic exercise) then you need glycogen to generate ATP.
If you're doing anaerobic exercise and you have sufficient glycogen stores then lactate build up can be moved to the liver and converted back into glucose, if you run out of glycogen though then it turns into lactic acid. For those who don't know what that is, it's the burn you feel at the gym that prevents you from lifting more.
So I really think looking at bioenergetics you really cannot effectively neglect carbs if you're an athlete. I think the majority of people whose health improved when switching to the paleo diet probably had an objectively bad diet and would've lost weight all the same if they had chosen better sources of carbohydrates, and used a better training program.
For bodybuilders in the cutting phase I think a paleo diet could be useful though since for every gram of carbs you need 3-4 grams of water for retention so a low carb diet can give you a harder look.