Playfulness shows up at work all the time, although not necessarily in ways that promote the bottom line.
Play mindsets can be encouraged in the workplace when they don't emerge spontaneously. Whether those efforts are successful for a given person on any given day...? It's still pushing a rock uphill.
Game design and reward systems are trying to find a path that doesn't suck. It may take another decade of experimentation before ten thousand failed attempts show the obvious and elegant ways to make more workplace leaders look like your favorite camp counsellor, recess organizer, or dungeon master.
It's more than that. The environment matters. Real play is risk free. You can do whatever you want and there are no consequences. This is not true for work.
At the end of the day business doesn't want their employees to treat work as play; they just want them to be more engaged while at work. But instead of looking at why their workers are disengaged they hire people who set up cute little games and contests and tell people to pretend they're not actually working. Which is all well and good until somebody drops the ball and they get fired. Whoops. Sorry Bob. I guess you didn't understand we weren't actually playing after all.
Gimme a break. Gamification is just bullshit newage snakeoil.
I wish my rainy day fund were that big.
You argue that sometimes work is "fun". I think a more accurate description is that work can sometimes be engaging. Like when you're presented with a problem that's right at the edge of your abilities but not out of reach. Yet it's still work. Unlike play, work carries with it stress and responsibility. There are consequences if you screw up. Worse if you stop entirely. None of these are true for play.
Gamification is bullshit because it encourages the perception that these differences don't exist or that they don't matter. It's a flat out lie. Work is not play. Accept it. Move on.