My best software designs happen when I'm taking notes on paper, and I think it's largely what you say - I can't write as fast as I can think, which more or less forces me to think more carefully.
The founder of You Need a Budget makes a similar argument about budgeting and not spending on credit - the financial limits encourage you to manage your entire lifestyle more creatively.
It's often observed that small, scrappy, hungry companies tend to come up with more creative solutions than large, well-capitalized corporations, and even observed that formerly small and creative startups seem to lose that spark as the money rolls in.
There's that section in The Odyssey with the island of the lotus-eaters.
Speaking of poetry, I suspect that many poets would say that their creativity is enhanced by working within the limits imposed by a poetic form.