Get hold of a book called Learned Optimism by Martin Seligman. Wealth does not protect you against illness, bereavement or relationship problems.
Doc, I really don't mean to sound dismissive of psychological study and the many theories contained within (I must emphasise the theory part).
I believe that given the appropriate subject of study, then it can help certain individuals to adopt alternative behaviours which might help them to enhance their standing and become more productive; particularly in the area of sport, where confidence plays such a big part in an athlete's ability to perform at their peak.
However, in everyday terms, there is no application of psychology which can benefit anyone until an event or an incident has occurred or taken place. The predictive rationale found in traditional sciences and conventional medicine are based on thousands of years of study and application and have been honed to reliably predict an outcome.
Psychology is still a relatively new branch of science and while it has carved a nice niche for itself, it is still subject to major scrutiny and questioning due to the vast array of variations in opinion and methodology.
Psychologists appear to be constantly at odds with themselves as they try to redefine behaviour and past theory - there slso seems to be extreme differences in the practical application of psychotherapeutic techniques.
You used an example of an 8-year-old not being invited to a party, but many psychological theorists would suggest that the vast majority of that age group are still very egocentric and not fully in tune with their environment.
I'm not qualified to determine the relevance of that theory, but an adult considering the wealth/happiness balance would have far more understanding of causal effect based on their experiences than an 8-year-old would.
If stress and anxiety are contributing factors to an individual's physical wellbeing, then access to cash riches would enable them to eat a more balanced and organic diet and live in a comfort more attuned to their health needs.
Money and wealth is not a sustainable solution to poor mental health, but a more balanced distribution of resources can be.