I think it depends entirely on one's definition of happiness.
If happy is being smiling and bubbling, laughing and kicking up one's heels... No you don't want an excess of that. One doesn't get an excess of irl, so an excess in fiction would be jarring, raise suspicions...
If happy is that thing you come back to again and again, the emotional high you crave, then yeah, show me characters having to deal with what that means in their life. Do they admit what makes them happy, or do they try and hide it from themselves? Does the society they live in promote or discourage their favorite form of happiness? How does that shape the characters view on how happy they are? Do those close to them know what makes them happy? Is it promoted or hindered? On purpose or by accident?
I think this is a brilliant question to ask if the writer asking themselves looks at it from the second definition! Our lives are lived without the promise of a happily ever after, my obituary isn't going to be "She lived happily ever after, the end. Will the family now join me at the grave side dedication, thank you."
Even if you look at life as a series of stories, when you accomplish one thing, you don't get a nice big musical closing number *que fire works and curtain call music* "we beat the tests and learned some stuff, now I've got my diploma and nothing's tough. Oh it'll be smooth sailing from here on in! I'm a qualified accountant and it's no sin, TO LOVE SPREADSHEETS FOR-EV-ER~~~"
Hell, I'd go back to school in a heartbeat if I could get my accounting certificate with a good show stopper. Biology degree with a nice moonlit pan out over inspirational number that all but guarantees a happy life traipsing through the jungle (that has no hindering government and provides life to the biologists studying it that is full of ease and comfort) making new discoveries for which I'll be remembered and loved forever.
^^^ not going to happen.
So. What do I get? I get to figure out what makes me happy. Not smiling happy, but living life by the teeth biting into each moment happy. "She enjoyed her usual state of ill health" "grinning into the teeth of the storm like a madman" "guilty pleasure" "unabashed joy" "but you love being miserable" "never more happy then when traipsing through misery"
If I can't find mine, I go to my favorite characters. How did they find theirs? Did they have it all along and not know? ([Expletive] ruby slippers, could have been home in act one) Did they stumble into it? Fate? What did those around them do to help or hinder their search?