You've Got to Approve Rhapsody for iPhone, Steve. Don't Be Pigheaded…Ow! Hey! Stop Hitting Me!

RealNetworks has submitted to Apple a free application that will bring its $15-a-month Rhapsody subscription music service to anyone with an iPhone or iPod touch and an EDGE, 3G, or Wi-Fi connection–assuming it’s approved by Apple, which is anything but a sure thing at this point.

Historically, Apple (AAPL) has shunned subscription music services, and fearing they might compete for dollars best spent on iTunes, made it impossible for them to interoperate with the iPod. A few months back, Apple would have likely done the same with Rhapsody, if only to tweak Real Networks (RNWK) CEO Rob Glaser, who infamously disparaged CEO Steve Jobs for his “pigheadedness” at the Digital Living Conference in 2005.

But things are a bit different today. With the Federal Communications Commission’s inquiry into Apple’s rejection continuing consideration of Google Voice for iPhone still fresh in its mind and the outcome of that inquiry still undetermined, Apple might be a bit more inclined to allow Rhapsody into the App Store. It certainly can’t withhold it by claiming it replaces core iPhone functions, as it did with the Google (GOOG) app.

And so we find Apple in a uniquely uncomfortable spot: Accept into the App Store an on-demand streaming music application that will compete for the attention of iTunes users or reject it and suffer further unwanted scrutiny by the FCC, not to mention a nasty public relations nightmare.