As I'm stumped again for a topic, I'm going back to another question posed to me on Twitter.* I'm expanding it slightly to give it more scope: "Can writing in one genre or medium help you or allow you to write in others?"
Yes and no. And bear in mind these are the words on an unpublished (and some would say inexperienced as a result) writer, and may therefore be entirely wrong and ignorant. If they are, please don't yell too loudly.
Writing in one genre will help you improve your writing, which in theory will allow you to do better when trying out different genres. You'll be better at dialogue, plot structure, pacing, description… and that will aid you. It can't not.
However, there's a limit to how much developing skills in, for a random example, urban fantasy, will help you if you decide to write a different genre. High fantasy, science fiction, and mystery are probably all fairly simple segues because the world building, the pacing, and the imagination are similar. Possibly also romance. But literary fiction? Memoirs? Political commentary? Those require vastly different techniques and approaches to what constitutes "book" and "research" and there's only so much writing knowledge that will carry over.** And someone who's really good at writing pop history will probably struggle with romance, at least initially.
And that's just if we stay with prose. Would writing prose help you write a stage play, a screenplay, or poetry? Again, with the plays I think there'll be a bit of crossover with characterization, but they're much more dialogue focussed and they have to keep the audience's attention, so writers really have to think about every line. It's a very different technique. And poetry's also difficult to do well. I can't even begin to talk about how different poetry is.
Can a poet write prose? Yes. Of course. It's been done. Can a playwright write prose? Again, of course they can, and do. And prose writers write plays and poems all the time. But it's going to take them a bit of work to do it well, unless they're a verified literary genius, and they'll likely get as much help from reading their second genre as they'll get from having written in their first. I also suspect that approaching prose from a play background will yield sparser, tighter stories, and a poetry background will yield more lyrical prose.
This is not to say that prose writers don't cross over, or that they don't do it well. Nora Roberts is a shining example. Janet Evanovich has an urban fantasy out. Everyone seems to be trying their hand at young adult and picture books. And I know of midlist authors who are old hands at both fiction and non-fiction. I think once you reach a certain level of skill, you can write just about any genre/medium you want and do well at it. Certainly, if you reach a certain level of fame, you can write anything you want to and no one will stop you because the books will still sell.
This is also not to say that writers shouldn't muck about in other genres. Each genre has different techniques which will carry over to all the others, and you'll improve as a writer by learning them. But should you try to excel at everything? In my view (and it's just my view), you'll probably be mediocre in everything. Better to specialize in one or two forms or genres, and you can dabble later once you've proven yourself.
So could I sit down and write a screenplay or a book of poems or a memoir? Yes. Would it be anywhere near publishable? No. I'm too new, too raw, and in the case of the memoir, too boring. Can you do all that? Of course, and power to you!
* By @worldofhiglet, again.
** I can see exceptions in people who've done intensive writing courses (BFA, MFA) in literary fiction or creative non-fiction, chose to write urban fantasy instead, and then decide to go back to their roots.