That's what I was doing at Palm, in 2000-2001. We were working on a Palm PDA (codenamed Jabba) that would have a built-in telephone network. (GSM, GPRS, something like that, I didn't work on the RF section). So yeah, back then, except for the camera, you could have done it all, have Apps (in an open development environment) all the usual PDA functions, voice calls and Text messaging, eBook reading.... Not sure about Music playing, but who knows what the future would have brought had the industry not crashed and taken out Palm.
I was working on a thing for "Remote Provisioning" that would allow one's service Provider to send you a specially formatted SMS message that would direct you to an update file and install it (In my documentation I strongly discouraged the use of the silent, automatic feature). But that would allow service providers to supply updates and new features wherever you were.
Unfortunately, in the process I discovered that Palm's TCP/IP stack was incomplete. While they had created and documented all the calls, they had only actually IMPLEMENTED the ones for the features they had needed in previous versions of the OS. And considering the Device/OS divide at Palm, there was little I could do about that.
Anyway, after they laid us all off, and split the company (between Devices and the OS, who'da thunk?) the thing actually came out as the Palm Tungsten M. And it was NOTHING like what we were working on. They added a frigging hard keyboard, fer cryin' out loud! But back then, Blackberry was the thing to beat.
Ah well, just another tale of woe in how I got boned in the Tech Industry. But the mightabeens are the real torture. (Price the market value of 1000 shares of Apple sometime and ask me why I hate Steve Jobs.)