"Living happily" itself is a myth. Nobody on this floating rock is consistently "happy" every single day unless there is something seriously neurologically wrong with them that makes them that way. Life itself is inherently suffering - this isn't some edgy edict, it's the fundamental nature of the human condition; we are animals, and moreso social animals, which, not unlike elephants, zebras, dolphins, cows, or donkeys, are biologically wired and adapted to chasing short-term fulfillment, and avoiding pain and suffering - to the degree we experience and remember negative feelings and experiences far, far deeper and longer than we do positive experiences. This is the telltale sign of our inescapable animal nature - the hardwiring that makes suffering so inherently unavoidable, and pleasure seemingly so elusive.
Boiling the phenomena of NEETdom down to "mental health" is a reductionistic fairy tale that completely ignores the context of modern life in favor of hyperindividualizing the consequences of that context down to the individual and leaving it there. Speaking of context - the factors you mention are not as much of an immunological force as you imagine. Our society is one rife with celebrity suicides, who so many see as the "winners" of our silly game - they have money, prestige, recognition, fulfillment, endless fancy toys and achievements - and yet still cannot escape the call to the void - which, if anything, speaks to the fact we spend our lives chasing things that really do not make our lives all that worthwhile in the end. Sure, it's nice to be clock in to your 9-5 every day and pat yourself on the back and tell yourself you're doing the right thing like everyone else, but this is the life of an obedient somnambulant - one we are conditioned for in this society. You know the script - go to school, work until you're old, save and scrimp the whole way through, retire, and go rot in an old folks home using the money you've hoarded your whole life. This might be a fulfilling life for an inanimate machine part that cannot feel and is not alive, but for a social animal that needs environmental enrichment and belonging and meaning to feel any kind of consistent fulfilment, it is a slow death. This isn't to say NEETdom is some grand alternative - it is the final consequence of this meaningless life program - narcissized depression and almost total alienation, whereby one practically declares themselves dead to the outside world and escapes deeper and deeper inside themselves as a solace, until the crushing emptiness of isolation and loneliness destroys their ability to experience pleasure and often their will to live. This is typically because of the self-isolating shame that attaches itself to the status. As social animals, we need people in our lives to feel any degree of worthwhile. Interpersonal interaction injects our lives with a kind of meaning and fulfilment that all the technology, distractions and drugs cannot. Unemployment and NEETdom would not nearly be as bad if not for the immense social stigma, and if we could all expect to live in communities we felt a part of, or at the very least had friends who cared about us outside of our job title. Unfortunately, this is not the nature of our hyperindividualized, materialistic, and vain society whereby one increasingly derives their (narcissized) sense of self-worth and status from their ability to consume and brag about said consumption. Instead, we live in a time where over half of the population reports always feeling lonely and having few if any friends, 1/6 of us are on psychotropic drugs, and the suicide rate hasn't been this high in 30 years.
All the same - this doesn't make "successful" people failures. But it also doesn't make NEETs "failures", at least in any individual sense. The failure is society itself - in providing an insane sociocultural script that makes people incredibly sick; if I could call NEETdom anything, anything at all, I'd call it the canary in the coal mine for a society that is providing an age old lifescript that is no longer worthwhile, rewarding, or even meaningful in any sense - nor does it even guarantee the barest physical necessities for participation anymore; recall that wages have been stagnant for 40 years and we have wealth inequality levels that mimic those found prior to the Great Depression, what becomes all the more clear is that modern life is the new Great Depression. This is a dreadfully sick post-meaning society where mass shootings, panoptic surveillance, suicide, opiate abuse, loneliness, and alienation have become as commonplace as psychotropic drugs and psych diagnoses; which, if anything, says nothing more than that the very concept of "mental illness" is a desperate attempt by the system to hold on to it's collapsing validity by pointing at dissidents and shouting "they have some inherent biological illness that makes them this way!" As such, the realm of modern day psychology/psychiatry has become no more than another long arm of the corporatocratic, neoliberal police state, which has a part in allowing modern-day quality of life to continue it's decades long slow bleed to the sociopathic class - the wealthy and powerful.
We must think of NEETdom, depression, and a wide scope of psychological maladies as meaningful signals our bodies are sending us about the ways we conduct our lives nowadays, not as noise that is to be ignored and medicated away." -David Foxxxy