One answer for improving cell phone coverage is to leverage local internet connectivity and use VoIP. T-Mobile had phones a while ago that had that as a feature. AT&T and Verizon's answer to this is microcells, which provide regular cell phone connectivity with the Internet as a backhaul. Of course, AT&T's microcell isn't available yet in most places. Adding the ability for phones to fall back to WiFi for phone calls is complex because of the relatively demanding requirements of full duplex voice conversations.
Most providers have a web page that can be used to at least send SMS messages.
I bet most of you are now way ahead of me.
It would be far, far easier to provide for SMS messaging over IP, because there are no demands for low latency or jitter. It would be simple for a phone to make a secure connection over an Internet connection provisioned with WiFi and use that connection to send SMS messages and poll for message delivery.
The carriers could even sweeten the deal by not charging for SMS messages sent over WiFi. Of course, given the obscene profits the carriers are making with SMS, the prospects of that actually happening are dim.