The next big idea? Battery charging stations?

To understand the question, you need a little background. Back when Bell telephone controlled the phone system, the phones where/are powered by (low voltage ) electricity from the power grid. More recently the phone service uses "cell towers" and switching stations that use power (a little of it solar). Cell phones are mostly powered by recharging batteries, from power off the grid. I got to thinking, millions (billions?) of watts of electrical power where/are consumed by the land line phone system, and an additional huge number of battery charging systems for cell phones.

In the big power outages in NY a few years ago, several million phones would not work! No power! The cells would work, but the cell towers and switching stations where down, except in rare cases where backup generators where working.

So my question is: If we changed the entire phone network to be solar powered. Quickly phasing out traditional land lines in most cases, and using solar/to charge the batteries powering most phones, cell towers, and switching stations, what would be the best, most economically feasible way to do that?