I feel like these explanations based on cognitive development always end up with unprovable assertions which inevitably support their author's views. The same exist about natural language, and they're always (unconvincingly) used to rationalize why language A is better than language B.

In my experience, when you ask people to tell you what "basic" operations they do for e.g. multi-digit number additions or multiplications, you get many different answers, and it is not obvious that one is better than another. I don't see why it would be different for languages, and any attempt to prove something would have a high bar to pass.