I'm not seriously thinking that this could actually be plausibly implemented in real life from the status quo we have now, so seeing it popularized in fiction is about the best I could hope for. So please, run with it!
I've been trying to come up with a modified version of it using six seasons / holidays instead, to match an internationalized six-element system (combining the western four and the eastern five) that I came up with while writing a (still unfinished) sequel to The Last Airbender and The Legend of Korra:
...as in that universe the seasons as associated with elements in a cycle (earth with spring, fire with summer, air with fall, and water with winter), and I'd like to extend that to this kind of holiday/season scheme. Also, six is just a nicer number than four, nice as four is. Since the fire/summer and water/winter connotations are pretty iconic, that would require the fire-air-water half of the year run from summer to winter solstice, meaning "metal season" would end on the summer solstice, the autumnal equinox would be in the middle of the "air season", "wood season" would begin on the winter solstice, and the vernal equinox would be in the middle of the "earth season". That way earth and air keep their spring/fall associations too, and there's something appropriate about equinoxes being in the middle of something. That does pose a problem for starting the year on an equinox, though.
And I'm not sure what the themes of the holidays for those respective seasons would be. The four holiday scheme fits nicely with the stages of life. What two more would we add? Maybe adolescence for the early summer (metal) season, between childhood (spring/earth) and young adulthood (late summer/fire); and then make early winter (water) season about senility (as opposed to the middle-agedness of autumn/air, but not yet at the death of late winter/wood).
So we'd have:
Spring/earth - For children (up to their early teens).
Early summer / metal - for adolescents (late teens and twenties).
Late summer / fire - for young adults (thirties and early forties).
Autumn/air - for middle-aged adults (late forties and fifties).
Early winter / water - for seniors (sixties and on).
Late winter / wood - for the dead.
But I struggle to flesh out any more details than just what demographic it's targeting. I'd think the adolescents and young adults would both be into the same kind of sex drugs and rock and roll party holidays, while seniors are likely to be reflecting on the same sort of things eternal that are for the "dead" holiday. How to split them up further?