As importantly, they retargeted the marketing. The iPhone was introduced as an entertainment and Web device. Prior to this, all the major players (Microsoft, BlackBerry, and Palm, as well as carriers) pretty much worked under the assumption that "consumers" weren't willing to pay for "premium" phones, so smartphones before the iPhone were designed for and marketed to "mobile professionals" with features like personal organizers and push email. At the same time, "premium" $250+ iPods were flying off the shelves.
But competing music players at similar price points were not, so I'd still tend to give more credit to Apple's execution than its "vision".
There were many other options, and as usual Apple simplified and minimised.