There is no reason a polymath cannot excel at all her interests enough to create careers out of all of them.
Take Benjamin Franklin. He was a Founding Father who started our country, a political statesmen. And yet he was also a scientist, inventor, and writer who contributed numerous inventions to improve our understanding of weather patterns, electricity, and even invented bifocal glasses. Or Leonardo DaVinci. He was a successful painter, sculptor, architect, scientist, mathematician, engineer, inventor, geologist, botanist, and writer. He excelled at all of them and is still well known for both his paintings and his mechanical inventions. There are many such people throughout our history. They may seem like gods, but so do Michael Jackson and Shepard Fairy.
I'm sure Michael Jackson made a great impact on the world and uplifted many millions of people. Is his work of lesser import than Ben Franklin's? You can't really compare them. They are equally important people, who hold significance to people in different ways. I think it is the systems thinking polymaths that will truly change the world, because they can see the big picture, how all the little interlocking pieces fit together to create the world. They can see what makes the world go round, and step in to make a difference.
I don't mean to brag, but I excel at both writing and science. I also have a knack for design that could be used professionally, should I choose. I am skilled at all three, but I can't do all of them at the same time. I feel, what makes me unique and powerful, is the combination of interests and skills that I let my heart embrace. I plan to see each of these fields bear fruit one day. On Scott Young's blog, he teaches something called Holistic Learning, which is making connections between seemingly unrelated fields. If you did not open yourself to other fields of inquiry, you could miss out on valuable connections.
It's true that if I focus on writing, my design will suffer. But at some point I will get bored, or tired, of focusing solely on writing, and that is when my design will bounce back. It's simply a matter of time, as my focus cycles through my various interests.
My legacy will be to have lived my life as fully and richly as possible, while contributing as much value as I can to the world. As Austin Kleon says, keep your side projects. "it’s the side projects that blow up."
You can also read my response to Mars' post here.