You're completely right. My girlfriend had two unpaid internships, and will have another before she graduates college (her college mandates her last semester be entirely a documented unpaid internship). She described it exactly as you just did - "paying your dues."

She has a dual major in business and arts, and wants to work on Broadway doing marketing or production work. I find it sickening, and it saddens me the way interns are considered a completely free, fungible, and exploitable resource just so they can get phony career advancement "at some point."