I’ve always thought silent movies and the radio were good examples of this. Silent movies had to tell everything with visuals and consequently developed some of the most purely “cinematic” films in movie history. Radio show writers and producers had to create entire worlds from sound. I’ve often wondered if the golden age of movies in the 1930s was a result of sets of people from these two creative backgrounds coming together.
Kant uses this image in “Critique of Pure Reason” - “The light dove cleaving in free flight the thin air, whose resistance it feels, might imagine that her movements would be far more free and rapid in airless space.”
I am not sure if this applies, but Steven Spielburg’s JAWs in generally held up to be a masterwork in the art of suspense and anticipation. I have read numerous articles stating that the decision not to show the shark until the 2nd half of the film was pure genius becuase it forces the audience to build up the animal in their own minds, and what we imagine is always scarier than what we see.
It later came out that the plans were to use the prop shark much more, but they could not get it to work properly and had to work around it. The faulty mechanical shark actually made for a better film.
Nowadays, we all the CGI, filmmakers really don’t have to get creative anymore, which could explain the more humdrum thillers we are seeing.
(By the way, I’m new round these parts - hi!)
A lot of director’s choices in film and stage are better when more limited. An unlimited budget gets you a Phantom or a Les Mis - which are entertaining shows, of course, but when you can afford to buy or build exactly what you want, tends to get very representational and not very creative. When you have $2000 and a cast of 10, you get really creative because there will be no show if you don’t. Mary Zimmerman (to use an example I saw recently) can create all of the Grecian Islands and a boat to sail around them on with a few 4X4’s and ropes. A few strings of Christmas lights become the constellations. Some burlap and a homecoming dress from the eighties make your wardrobe. And it’s a far more creative - in the sense of creating original stuff, and in the sense of stretching your brain - endeavor than when you can simply go out and buy what you need.
Furthermore, the limits of your stuff increase the creativity of your AUDIENCE, not just the artist. When the audience has to fill in the blanks, they become part of the creative process. They become involved, rather than observers. We all have our scariest/sexiest/grossest/funniest things ever, and if the director can get us to project that into the performance, we’re all working at a level of superlatives, instead of shrugging and accepting the director’s vision of “ugliest” as reality.
The classic example, of course, being Psycho. Everyone thinks they remember the knife stabbing the woman. Didn’t happen. We filled that in on our own, because Hitchcock wasn’t allowed to show it. And because we filled it in on our own, it was our own version of scariest.
Acting in opera benefits from this same “limit boost,” in my experience.
Any kind of acting other than improv already has a limit on the performers creativity: the script. But they are still free to make decisions about tone, timing, and overall expressive intent. Two different actors inhabiting the same role can make wildly different choices.
Once you add music to the mix, however, those choices have already largely been made by the composer, and so your creative energy is channeled into making those choices work as dramatic moments, rather than making the choices themselves.
Having to bring someone else’s dramatic framework to life so that it seems organic and spontaneous to an audience forces you to commit to that framework and to its underlying choices in ways that you sometimes don’t when you’re free to make them yourself.
On rereading, I don’t think I’ve said this very clearly, but oh well! 
I think it applies perfectly. And welcome!
I guess this is only a little bit what you are asking about. I find that when writing technical papers it goes so much more smoothly when I work from a pre-defined template. As you said, I don’t have to put any thought into structure.
Well, Robert Frost said
Pithy enough for ya?
Y’know, I think this thread is giving the most compelling defense of fanfiction I’ve seen in a long while. 
(Although, to be honest, eventually it does stop being fun playing around in other people’s worlds and the idea of building your own gets a lot more attractive.)
A little limitation absolutely helps spur creativity. I’ve never been able to make something up out of whole cloth, but I consider myself very good at taking the germ of an idea created by someone else and expanding on it and fleshing it out.
A little limitation/structure:
- Provides direction. With total creativity, either it can take too long finding a path that works for you, or you find so many paths that work that indecision inhibits growth.
- Gives you a sense of what works and what doesn’t. If you’re working freeform, it’s harder to tell when something works or fits into the overall picture than when you have a rule or two defining the boundary.
Fanfiction is definitely a good example. Granted, there’s thousands of terrible writers who couldn’t have an original thought if their lives depended on it, but it’s also a good way for emerging writers to practice the actual act of writing plot without worrying about characters or setting. The trick, though, is acknowledging and accepting the constraints that writing for a premade world imposes; bad fanfiction arises when the writer does not accept those constraints (personal characters being the most powerful characters in the story, unlikely romances, and other such horrors).
Shakespeare certainly didn’t say anything like the idea in the OP. It’s just not the sort of thing he would say. I presume that the quote given above from Robert Frost is what is being asked about.
I hate that Frost quote.
If I’m playing without a net, that means my opponent is, too. And that would simply make the game harder.
And exactly how is writng poetry like playing tennis, anyhow?
A common example we’ve all encountered is in party games that engage our creativity, like charades. There need to be some rules and there needs to be a chosen thing to pantomime before the whole thing really takes off. Everyone can play charades within those limitiations – but if you just out of the blue turned to the person next to you at the party and said “act something out,” he’d be dumbfounded and have a hard time getting started.
Sailboat
As an actor and an improv comedian, my personal experience is that limitations, even self-imposed, encourage exploration. If you are a creative personality, once you know a thing, you are basically uninterested in it. You need to explore beyond it.
A “limitation” is a fact about the world you’re creating that you already know, it is inalterable. One of the most satisfying questions to answer in improv or in any other creative pursuit is:
“Given that this is true, what is also likely to be true?”
It’s almost like exploratory science. Here are the rules in this universe, they are arbitrarily defined, you cannot change them, what does this lead to? I get tingles thinking about it, honestly.
In less esoteric terms, I think of movies like Primer and Cube- both defined and in a sense inspired by their limitations in resources. Cube was written specifically as a thought experiment- how can one make a sci-fi/horror movie with a small, unknown cast and a single set?
A rather mundane example would be Scrapheap Challenge (Junkyard Wars in the USA) - creativity in design being provoked by the limits of materials and time available.
Or The Great Egg Race (who remembers that?) - where contestants had to build devices (initially egg-transportation devices) out of very scant materials such as drinking straws, newspaper and spoons.
I dunno … maybe you play little mind games with reality, then set yourself to try and match your perceptions with words as best you can?
A simile, like a witty joke, loses all it’s magic when it has to be so bluntly explained, so I hope this question is rhetorical. Nevertheless, Frost is intimating that tennis wouldn’t be much of a game without the limitation of a net in the middle, just like poetry isn’t very interesting without the limitations of verse form.
I once asked a moderately successful artist (she earns enough to eat and pay the mortgage) about this. Her answer, “You have to know all the rules before you’re good enough to break them.”