After reading your post and rereading Godin's post, I realized that he doesn't talk about connections. In Godin's world, we're doomed in those jobs. We gain nothing from them. You get it. These jobs are learning opportunities, and they're prime spots to make connections.
I think it's important to note something else about these jobs: real world experience. College programs can't teach you everything about the business. Budgeting is a major point. Ignite might want to produce a new playwright's work, but the budget doesn't allow it. When you're inside the organization, you learn about these types of decisions.
So just ignore Godin. He's a brilliant marketer, but this business is about connections and insight. Get a job at theatre or agency, and make friends. I know many professionals that started in another part of the industry, but they made the right friendships to launch them into new jobs.
Plus...a person might actually like his or her job. Who knows?