You haven't stated the security problem you are trying to solve, so I'm going to default to "defeating government snooping".
There's no reason this wouldn't work from a technical point of view, though from a business perspective it is impractical and would get very few takers. The primary problem with it is that it will be challenging from a wifi access perspective. Mobile telephone companies have spent billions on the infrastructure to establish quality coverage over wide areas, you're talking about people giving that up in favor of wifi services that are spotty even in metropolitan areas. I personally wouldn't use it.
Also, in order to really ensure privacy you'd have to develop your own mobile telephone OS, and prevent it from going to any app stores. Who knows what back-doors the mobile company put in the android distro they put your phone? Installed apps can have all sorts of snooping capabilities, so if you don't control for these things there's no point in your design.
Lastly, say you build this and some people start using it, nothing is going to stop governments from knocking on the VoIP provider's door and demanding that they give them their phone records. In fact, in many places any phone provider is already compelled to by law. So you'd be substituting snooping on mobile networks with snooping on VoIP. The fact that you are going to put these calls into the phone system at all defeats the whole purpose. Information from the VoIP provider could be used to determine the location a call was made from using the IP addressing used in the VPN that was set up. You could obfuscate that by running some VPN proxies for people to connect through, although being that they'd have to be set up beyond the reach of the government you're trying to defeat you're going to have latency issues.
If you want to deliver secure communications then encrypted point to point connections are a good way to go. You can use mobile providers' own networks or WiFi for transport, whatever's available. Network availability would be much better than if you rely solely on WiFi. It doesn't matter that it goes over the mobile network as it's encrypted, and if there are secure servers somewhere out there to act as proxies (think TOR) then the end points of the connections are harder to track. Not that Skype already does much of this, however their operations and code are closed, I personally wouldn't treat it as secure or private.