“…fatter necks actually are better suited for proper playing technique (thumb in the middle of the neck, playing with tip of curved fingers)."
Define fatter? And what shapes are these necks? As C/D/V/Asymmetric etc all have very different feels as far as the thumb goes. Are slimmer necks better suited for certain carves? And how does nut width enter into it? Take a 6 string bass, how fat are you wanting that neck, as they are usually very flat in comparison to a 4? As a standalone sentence, your claim here isn't substantiated.
"The distance from the pushing fingers gets smaller to the string and the hand gets a better grip or “strength” thanks to a more solid contact to the actual neck."
I honestly don't know what you're trying to say here to refute it. If you can reword it I'll have a go!
"Less “air playing” equals less distance, more strength, less movement with the resulting increased control…thin necks are not “faster” or “smoother” or “better” for anyone but someone with REALLY small hands aka: children” "
Again, for me the nut width/width of the neck and the carve shape has a much greater impact on all of this than the depth of the carve. How "fast" a slim neck feels is entirely subjective to the person and their playing style and technique. Certainly not just for people with REALLY small hands.