I guess you can do whatever catches your fancy if you're Richard Feynman. For the rest of us mortals, the challenge is in finding interesting stuff to do within the constraints of the environment we're working in.
The lesson that I take from the quote is that you've got keep yourself interested in whatever you're doing. If getting up in the morning and turning up to the lab seems like a chore, then something needs to change until it isn't.
That's when I wrote FreeBSD Update and bsdiff, and found new algorithms for matching with mismatches and feedback-free file synchronization. In hindsight, that was probably the most productive year of my life so far -- and all because a life-threatening medical condition forced me to step back from the project I was working on.
Now, you might want to avoid getting hospitalized or losing several years of life expectancy; but I still recommend taking at least a few hours a week to explore new directions. If you got hit by lightning, your colleagues would find a way to replace you; if you get hit by a bolt of inspiration and run off to win a Nobel prize, the same applies.
Anecdotally speaking, a lot of the creative and playful people I know seem to spend their careers moving, incrementally of course, from less autonomy to more autonomy. I see these moves happen when people leave a job, accept a new job, start a business, switch majors, transfer universities, or apply to specific grad program.
My point is that it could have been something essential to Feynman's character that led him toward the amount of autonomy he's famous for having had.
"Up to about 1950's there was a kind of freedom in the scientific world — certainly at MIT — that allowed you to play games of all sorts. As two or three decades went by MIT was taken over by managers."
"Managers have wrecked education immensely. The differences between education and research now and what was done 50 years ago is fantastic. There's a profound difference in the freedom to research and question that you could do then, and what you're not allowed to do now. I wouldn't be able to get a job now under any circumstances."
BTW, one of his hacks showed up on HN a while back. (http://apps.ycombinator.com/item?id=2670243)
There is a great section on "Surely you're joking, Mr. Feynman" with Feynman describing burnout. From what I took from this was play as such wasn't time out from commitments but a different way of approaching problems. If you get bored it's a chore but if you play it's not. Read this extract (pg. 157-158) to understand ~ http://pages.swcp.com/pcaskey/feynman.html
Also, academia encourages you to think in terms of the theories/dogma/paradigms of the day, in order to relate to the literature, to get published, and to get funded - as you say (it's a market, but not based on actual need). This is very effective for incremental improvement, but makes it harder to be truly original (which is hard enough already).
Yet, within any environment, there are constraints but also some freedom. There's a choice of approach to that free time: adapting yourself to your environment, or using it for play.
There are also some other good stories in that talk, one about Marvin Minsky which immediately follows the Feynman story. The whole thing is worth listening to, I think.
I find that when I reach that point, it helps to take a break, look at the problem with a fresh mind, and try to break down the solution into smaller pieces. At that level, some parts become interesting and fun again, even though others might not be. At least you have fun in some of the parts, instead of feeling the grind of the entire thing.
Some of my biggest breakthroughs on work-related projects have come to me as I've been hiking, taking in a museum with my wife, or pushing my daughter on a swingset.
Bart: You're making me lick envelopes?
P.S.: Oh, licking envelopes can be fun! All you have to do is make a game of it.
Bart: What kind of game?
P.S.: Well, for example, you could see how many you could lick in an hour, then try to break that record.
Bart: Sounds like a pretty crappy game to me.
P.S.: Yes, well... Get started.