An interesting post, and above all, a sentence to remember:
And to do two difficult things at the same time doesn’t make it twice as hard, it makes it ten times as hard.
The author wrote it about scat singing, but it applies (maybe even better!) to instrument playing. I can't tell if the numbers (ten) are right, but the general idea is right.
Well, don't take it too seriously; any jazz musician could (should) think that improvising is not such a big deal. But you can bet it's not easy.