I had never heard of that as a cell based system, but, after doing some research, sounds like a novel idea. One downside is that you have to setup the WiFi connections you frequently use, unless you download an app that connects you automatically to some public WiFi hotspots. Upside is if you are in an area with high population and lots of WiFi connections available, you should be able to quickly identify the ones you use. Another upside is that all cellular based calls are through the Sprint 3G network. Downside is cellular calls are on the Sprint 3G network, which, in my opinion, isn't the best network available. But, with more and more companies and even cities taking on WiMax and offering wireless internet covering large areas, this could take hold. Downside is network speed on these calls could be an issue, especially if you are using your home WiFi system while your wife/daughter/son are also surfing the internet and taking up bandwidth.
http://www.boygeniusreport.com also states that the "unlimited" plan available and being offered is a beta version, and Republic reserves the right to change the limits of the plan in the future.
Our company is currently installing a WiMax system that will be offered to anybody within a 5-mile radius of our existing radio tower. I am going to pass this info on to our IT guy and see what his thoughts are. Since our company cellular bill is roughly $10,000 a month, reducing this by any percentage and using our existing wireless network makes perfect sense.