The most obvious, and significant, argument in favor of paleo is that it tends to make it more difficult to overeat or maintain a lot of weight (i.e., it's acts as a fail-safe against akrasia). Imagine if you only had nuts, fruits, and vegetables to snack on and for anything else you had to cook a meal.

A better diet would be to push your eating window to 2-3pm to 10pm (intermittent fasting), and only eat low calorie things which you've cooked (and make sure you don't buy anything that can be eaten without being cooked).

Basically, from the research I've read, akrasia is the most significant factor in maintaining a healthy weight; anything you can do to force or impel your future self to commit to your non-akrasiac desires is a good idea.