I see this as a way to get more experimenters to be hams. It also makes it much easier to demo explain / teach / get people excited about SDR and what you can do with them.
I could imagine this being a cheap platform for crisis regions where radio transmission channels are run by government (or not existing at all).
"Important Disclaimer: While the output power is very small, you should still take great care as the carrier is a square wave, and there is no filtering on the antenna output. So any transmissions will cause harmonics all across the spectrum – possibly interfering with life critical devices. A filter must be used if you actually plan on transmitting with any sort of range further than your room."
There's a lot of filter adjustment, antenna tuning, and shielding placement as you look at a spectrum analyzer and see spikes that shouldn't be there. This is why there are little RF modules in cans for many applications. Someone already did that work for you. Some vendors: 
HackRF Blue: http://hackrfblue.com/ ~> $200
rad1o (HackRF from spare parts): https://events.ccc.de/2015/07/10/rad1o/ ,
http://hackaday.com/2015/07/12/cccamp-2015-rad1o-badge/ ~> $100?
That would only give us half duplex. If we want to simultaneously transmit and receive, I guess we could add an RTL-SDR. ~> $10
Plus antenna(s). $ $ :)
The DAB iniatives doesn't seem to work out (eg Canada) though the lobbyists are still strong. Analog radio works even with bad signal quality (https://en.wikipedia.org/wiki/Digital_Audio_Broadcasting )
Just to make sure I get this right, a "wire antenna" is just a wire, right?
Somewhere in the posts is a suggestion to build a lowpass filter and that will work. But the Pi puts off some pretty messy spectrum splatter, so before you build a good antenna take a few mins and build a narrow passband filter. It cuts the splatter below (like a lowpass) and above (like a highpass) your chosen frequency.
Better yet, go to QRZ.com and look up a ham in your area to help you out. We have parts in our vast inventory of supplies (aka junk box) to help you out.
For more powerful equipment getting the wrong wire geometry could melt your expensive setup and get you in trouble with the FCC, so it makes even more sense to tack on the word "antenna" to mean "I've thought about this chunk of metal outside the DC approximation."