EDIT: [I can't reply to the comment below, so I'll add here] It's most likely not a technological problem, but rather than data usage is limited on mobile and you don't want your user to pay for traffic they didn't use.
Primer concept: http://en.wikipedia.org/wiki/Interrupt_coalescing
Pricing: Most people in the US are charged for the data they use on their mobile devices, and thus would not want P2P used on their phone because it costs them money.
Spectrum: P2P is not a very efficient distribution model in a world where most clients are on asynchronous connections. Asynchronous connections exist because transmission spectrum is limited, so to maximize spectrum usage, telcos allocate more spectrum for downstream transmissions than upstream. But if everyone's phone is chattering all the time with P2P traffic, you're going to saturate the spectrum and reduce overall data speeds. This is why mobile is still charged on a usage basis: it discourages overly chatty applications.
The big hurdles I see are (in no particular order):
- Connection maintenance and keep alive. Basically this is bad, so you want to be more aggressive about shutting down unnecessary P2P links on mobile than you need to on desktop/server. Keep alive requirements generally suck anyway, and are one way NAT murders kittens.
- Restrictions around background tasks on mobile OSes (iOS is particularly onerous).
- Squelching inbound traffic from badly behaved or broken peers to avoid inbound flooding.
- Battery life and related concerns.
I understand it this way: cellular networks currently have their own "netiquette." It includes things like don't be too chatty, try to coalesce instead of spewing packets at excessively random times, etc. These things are less important on wired networks since they don't have the same resource constraints or bandwidth issues.
I guess a related question is why you would do P2P and not backhaul to the cloud? I can think of many:
- Reduced latency for things like AR and VR where latency matters a lot.
- Reduced bandwidth cost due to lack of back-haul, and back-hauling a pic being sent between two people in the same city 2000 miles to a cloud server is just offensively stupid anyway.
- Privacy and security.
- With P2P you could have a more open app model where apps aren't wedded to proprietary cloud infrastructure. They still work even without someone's cloud, etc.
P2P over non-cellular (i.e. Wi-Fi or Bluetooth) where you can actually make a direct device-to-device connection seems like it may have some use cases (messaging apps, etc.) But they're edge cases and by no means a common use case because it just isn't reliable enough.
Skype has abandoned P2P, though I'm not sure why. One possibility is that MS now has middle boxes deployed at so many interchange and peering points that there's no benefit in maintaining the added complexity. Another is that it was to comply with surveillance/tapping requirements.