If I were Obama, I'd want him to be Arts Czar in a cabinet-level position.
He's actually a member of the President's Council on the Arts and Humanities. A few years ago, he and Heather produced a wonderful "day of dance" at the White House for area children which was live-streamed. (The White House studiously avoids the word "czar" - that comes from the press and the President's critics.)http://www.pcah.gov/members
The Arts Endowment has a brand-new Chair, who seems to be quite good, Jane Chu: http://arts.gov/staff/jane-chu
It's a monstrous responsibility (as Jane Alexander wrote about in her book "Command Performance" after she was NEA Chair during the Clinton administration). And as the new Chair at the Humanities Endowment is a white male, it would have been difficult to appoint another white male just now at NEA. Woetzel seems to have so many interesting irons in the fire, he might have been reluctant to take it on, if he had been asked.