It is a convenience they have to pay for. Banks charge INTEREST and FEES to merchants to process credit cards. And the banks are upping the rates. And banks DON'T offer discounts for volume unless it is prearranged in advance(i.e on the same day like when AutoPay is done) in so it costs them MORE money if everyone starts using Credit/Debit cards to pay. So it would not surprise me if they CAN process checks cheaper then they can CC. If you want to blame someone blame the banks. They are the ones charging more fees ontop of huge interest rates. VZW is just trying to cut costs.
It would absolutely cost them more if everyone paid by check. Do you know how long it would take just to open millions of envelopes a month?