One point that isn't directly mentioned is that he was able to turn the 'wobbling plate equations' into a Nobel Prize because he had such a wide breadth of knowledge to draw from, and probably had a habit of drawing parallels between what he's doing and other things within that breadth of knowledge.
He wouldn't have even thought to make the parallel between the wobble and how electron orbits move in relativity if he didn't already have a good understanding of electron orbits, and it wouldn't lead to the Dirac Equation in electrodynamics without him being familiar with that, then quantum electrodynamics without being familiar with that.
So yes, while play and working on things 'with no importance' can lead to great discoveries, or something of importance later, you need to have that background of knowledge and the habit of connecting two disparate concepts together or else it will always remain something 'with no importance'.
I was being facetious though. While the story is interesting, it should be considered in the current context.
A huge swathe of senior researchers are burnt out but the wisdom Feynman imparts isn't particularly helpful to them due to the nature of academia today.
I think you can still use Feynman-like play in academic work, you just have to pretend to the funding people and the MBAs running the university that you're "totally serious", that your work can be turned into money etc.
I have a few scientific projects that I play around with when I'm stuck on my "totally serious stuff I'm supposed to work with" which give publications at some point, but that's more of a side-effect than anything else.
And of course scientists now bullshit an extraordinary amount when it comes to future applications of their work - they often don't particularly care, the MBAs just want to hear their mantras.
The first part sounds like a play on the Picasso quote "All children are artists. The problem is how to remain an artist once he grows up"[1] and the second half sounds like something Ken Robinson said in his TED talk about creativity[2].
What's interesting about the underlying implications of all these quotes to me is that what makes a good physicist, a good artist, or a good anything, is the unabashed curiosity, a willingness to experiment without being stopped by fear of failure, and the state of play that one must be in to unleash creative approaches and new connections.
Assuming personal projects... Use cheap and simple PAAS integrations. Don't write documentation on a personal project. Only test the complex stuff that touches a lot of your app, and enjoy the new ways it challenges you to conceptualize. 100% test coverage is foolish. Don't "test like the TSA." Actually, don't even write tests if your app is simple.
Code however you want. Don't let programmers who pose as authorities fool you into thinking you're 'doing it wrong', that kills all the joy in programming. As long as you're thinking through things and it works, and especially if you're actually enjoying it, you're most certainly doing it right.
Deployment scripts, documentation, and unit tests can be fun too - the problem is that our attention is usually (rightly) on the problem we're solving, and so all the boring stuff feels like a distraction. If you really delved deeply into how to make deployment & testing as elegant as possible, there's ample room for creativity there.
He started out having fun with physics, worked very hard to accomplish tangible things with it, and burned out because that made it stop being fun (to the point where he found it "disgusting"). He started playing again, doing things that were completely useless, and that lead to his greatest discovery.
He wouldn't have even thought to make the parallel between the wobble and how electron orbits move in relativity if he didn't already have a good understanding of electron orbits, and it wouldn't lead to the Dirac Equation in electrodynamics without him being familiar with that, then quantum electrodynamics without being familiar with that.
So yes, while play and working on things 'with no importance' can lead to great discoveries, or something of importance later, you need to have that background of knowledge and the habit of connecting two disparate concepts together or else it will always remain something 'with no importance'.