Why is it that nobody’s marketing broccoli and bananas? This stuff is sold in stores, in exchange for money. Presumably there are for-profit enterprises out there with a vested interest in selling more.
That's from Matt Yglesias. I suspect the core reason is the absence of branding. "Got Milk?" only gets you so far. Most promotional campaigns ("green, and really good for you") will benefit all broccoli sellers, rather than any particular brand of broccoli, plus the profit margin on broccoli probably isn't so high anyway. (By the way, "Got Milk?" has statist origins.)
Here's one broccoli commercial, it's — dare I say — really stupid yet it is #1 on YouTube for "broccoli commercial." Here is Bill Cosby's "tribute to broccoli" — it remains unaired. If you watch it through to the end, you'll see it's actually a Jell-O commercial.
You could spend quite a bit of time watching ineffective broccoli promotions on the internet. At least this one appeals to some Hansonian impulses.