Text Your Bill Venmo.com
thedp.com
thedp.com
It has been done before, but it hasn't caught on yet in the US. I'm not sure why. It does fine elsewhere - but the configuration is usually through the carrier.
This isn't US-specific, but according to the PayPal interview in Founders at Work, the problem is fraud.
I think this is a user issue. People don't currently pay with there phones. There are a bunch of options for it.
Venmo has been getting quite a bit of buzz lately in my circles so I'm sure they're on PayPal's radar.
But what happens if you don't have a venmo account and you pay the restaurant and then decide when you get home not to create an account? Do they somehow charge you through your phone bill?