I've been talking about my taste in yarn at the store, in relation to the sweaters that I've made and what I'm working on now, and through intention or happenstance I've discovered that I've been working with a constrained palette for some time, and as I'm thinking about the projects that I'm working on now and what I plan to be working on in the future, I've caught myself thinking about this kind of creative exercise in a slightly broader context.
Knitting with smaller selection of yarns does something really cool for me as a knitter. It means I can think less about some of the trivial things: how many stitches do I need, or how will this look when I block it, are questions that I don't have to ask, because I'm used to the yarn a lot. Furthermore, I think with more experience I can and do get better at designing and working with the yarns, and I know that my core of yarns is quality stuff that will hold up for me long term.
And there's always the adage that scarcity produces creativity, and I'm willing to buy that. In a lot of ways science fiction presents some interesting constraints. In my current project, most of the story occurs on outposts and long range space ships, where there are limited resources and populations. It's not the same as constraining your word choice, or something on that level, but it does mean that problems that you and I might solve by running away and relocating have to be dealt with in another way (I'm mostly think of public health disasters here, but it works in other situations as well.) I'm not sure that this is best example, but it's a start.
I imagine that there are other kinds of creative constraints that we place on ourselves. I imagine some people write long hand for this reason (even if they're crazy!) and indeed choosing to write a story from a particular POV could be one of these constraints.