I do not want a mobile phone, but are there any issues I'd run into by developing games on an iPod for iPhone?
There is no problem with developing for the iPod touch. Most testers had those as primary hardware where I worked before.
One thing the iPhone was used for (apart from specific hardware bugs) was incoming phone calls. But now you can simulate those on the ipod touch with FaceTime.
I think there were months where I had only iPods with diferent iOS versions during dev. The iPhone is definitely not mandatory.
Hope this helps.
Edit: Actually due to the memory limitations it is a much better idea to develop for the iPod touch rather than the iPhone. This way you will deliver a product which will run properly on a larger number of devices.
You will not be able to test or run higher end games and graphics as the iPod Touch hardware has not been kept up to date with the latest iPhone and iPad hardware. If you are only interested in simpler games and graphics, though, there should not be a huge issue. You'll want to have some friends test your game on the other iDevices before publishing it, though (always a good idea in any case).