I've seen that in some cases the definition of mental health will explicitly score against things like "lacks close relationships" or "does not seek companionship". So it always seems to me a bit circular to just assert "being more social is more mentally healthy" when the definition of mental health bakes in "being very social".

If I were to define mental health to include "desires and enjoys spending lengths of time in solitude", then I could assert "Humans as a species crave solitude, mental health is shown to directly correlate with the drive and ability to be alone."

Why not define poor mental health as "puts a gun in mouth and pulls trigger" and then see if it correlates with things like "lacks close relationships". Probably a better method than 'making shit up as you go along' people that want to prove a particular point tend to do.