I hesitate to contradict someone who has gone through the whole Math PhD process, but I have to say that the best mathematicians that I know treat the problems they're working on as games, or riddles to be solved... and they've taught their kids (and others) this same method of thinking about these problems. There's a huge mental tool set, and often a lot of grinding to get to a solution, but it's just a game (and there are often more elegant solutions)!
I enjoy provoking interest in complex numbers and exponentials among precocious teens, but I've never been more humbled than having a Galois theory joyously explained to me by an 11 year old. (p.s. I'm an engineer so I follow your technique).
To me the problem isn’t learning it, it’s retaining it.
I learned all kinds of quantitative analysis and statistics in the CFA program ten+ years ago.
I had daily sheets that I would solve equations and answer all kinds of questions. I knew them forwards and backwards. I just looked at one now on fixed income - not sure if could answer any of the questions today to save my life.
I don't think you're contradicting the GP. Solving problems for fun still counts as "pressing need".
The alternative is something like "Oh, I should learn abstract algebra because it's a fundamental course in all curricula". You'll learn it, and then forget it.
I enjoy provoking interest in complex numbers and exponentials among precocious teens, but I've never been more humbled than having a Galois theory joyously explained to me by an 11 year old. (p.s. I'm an engineer so I follow your technique).