Rants on social media are an easy outlet for frustration and should not be conflated with insightful opinion piece journalism.
IIUC, he implores educators to optimize for productive "workout" rather than fun. From my point of view, "workouts" must be rewarding on average, but need not be fun.
I can't think of a single instance of learning a subject that mattered where I would describe as "having fun". Let alone too much fun.
Only on games which are fun themselves I could describe them as a fun experience, but they don't really require deep learning. The ones that do, will often stop being fun too.
It's very easy to enjoy the first stages of learning and have fun with it, but to really learn something, you have to get past that phase. Then it's much more about repetition and grit, than it is about fun.
So, for me, too much fun == not really learning.
Karpathy clearly wrote something different that what you say he wrote.
Here's my take: "Learning is not supposed to be fun."
"Not supposed to be fun" has a clear meaning. "It doesn't have to be actively not fun" doesn't have a meaning. No one ever says "actively not fun". It's a cop out to pretend like he's not presenting a false dichotomy, and I can see right through it.