Even if the characters wanted to get professional help, There Are No Therapists to help them with the issues they develop trying to save the world.
Inverted: All characters are some of the most stable, mentally healthy individuals of the world.
Subverted: Bob complains about his parental issues, depression, and unhappy life, but he is actually practicing for a monodrama. His wife, Alice, seems to be dissatisfied with her family life, but after the bad day had passed, she is back to her normal self again.
Then they begin to get issues over the course of the story.
Parodied: Everyone is loaded up with issues and angsts it up like a hammy actor, when not acting Cloud Cuckoo Lander style crazy.
Zig Zagged: Everyone has issues, except they were just method actors pretending, but they have other issues instead that get therapied away, but resurface later due to a series of suspiciously coincidental tragedies, but it later turns out It Was All Just A Dream in a plot by the Big Bad to break their confidence so he can take over the world, and to get out of the dream they have to truly overcome their issues once and for all, meaning that when they escape to save the world, they are emotionally nigh-invulnerable.
No one has any issues, and everyone is able to deal with work and day to day life effectively.
Or at least most people do.
Enforced: "To create more drama, we need the characters to have issues. Lets make everyone from a bad neighborhood, abusive family, or just plain have mental illnesses".
Lampshaded: "You would think that there would be at least one or two people here without issues."
Invoked: The Five-Man Band feign this in order to confuse the Big Bad into thinking they're too dysfunctional to be a threat.
Defied: Everyone has issues, but realizing this they agree not to let those problems rule their lives, and use as clear communication as they can.
Discussed: "I think it must be 'misery loves company', there's no other way to explain how all the people we know and befriend are as messed up as we are."
"I wonder why those people don't try and get group therapy discounts?"
"What's amazing isn't that everyone has issues, but that they somehow haven't torn each other a new one or left in search of saner friends."
Deconstructed: Everyone is so screwed up that they're completely unable to do their job, or live day to day, possibly even becoming prone to dying.
...But they are stoic and strong-willed enough to do their jobs without succumbing to their problems.
But working together (in a non-Epiphany Therapy manner), they manage to slowly deal with their problems one at a time and heal emotionally/mentally.