Partly right, partly wrong.
AT&T has publicly announced that it would like to abandon the old copper POTS network by 2020. And, yes, that means not upgrading something that they are trying to get rid of. The company's stated goal is to have fiber in the vast majority of areas by then to replace the copper, although I think at least in most cases the copper will still be the actual physical connection at your home or building's NID.
But the reason is almost certainly not to push cellular broadband on a wide scale. Cellular uses up a finite resource of very expensive wireless spectrum. It's much better to transport fixed phone and data over fiber, and save that spectrum and capacity for mobile users. The main reason to get rid of the all-copper (TDM) infrastructure I believe, is that if you are limited to DS-3 backhaul into an area, at best it only lets you sell phone or DSL service, whereas a fiber-driven infrastructure (all the way to the curb, or at least fiber to the neighborhood and copper for the very last leg of the trip) lets you sell cable TV services, high-speed Internet, etc. That's what FiOS and Uverse are.
From what I understand, the idea is only to push cellular broadband as a replacement for USF obligations where it is cost prohibitive to run fiber (think rural areas). That at least would make much more sense than trying to get everyone to go wireless when you have a perfectly good wireline connection to use.