Of course every carrier wants you using wifi instead of their network. Its not their expense, but you would still be paying them for it. But people are not subscribing to often ludicrous mobile plan bills to be told to not use it.
We absolutely have the technology to provide a huge swathe of people broadband (as per the new FCC relabel) Internet access through long-range transmission based tech like GSM CDMA or WIMAX. That makes it insane to propose laying physical wire in the dirt or making an interconnected mesh of low power wifi routers as a substitute. The only real barrier is the draconian privatization of photons that makes up spectrum regulation. If we had a 95% open spectrum with some restricted for government and emergency communications you could easily have broad spectrum towers that could adapt to congestion and pair them with radios that will adapt frequency to optimize for range vs data rate vs congestion.
The limitations are entirely artificial and that should be pissing people off.
I'm still on the fence about de-privatizing spectrum for a variety of reasons. But the biggest elephant in the room whenever discussing spectrum de-privatization is that the FCC earned US$45 billion from wireless carriers last year, and US$19 billion in 2008's auction (http://www.cnet.com/news/fcc-rakes-in-45-billion-from-wirele...). In the grand scheme of the entire US federal budget, I think that's just a drop in the bucket. But it's still money that the federal government looks forward to.
So on the one hand, the FCC wants to play fair for consumers and tax-payers. On the other hand, the FCC can't really restructure an existing industry without biting the hand that literally feeds their existence to the tune of US$2-3 billion per year if you imagine their auction revenue as ratable over the years an auction doesn't take place.
Obviously we can look at the FCC and know it will not actually break up the spectrum monopolies, because its a conflict of interest. That doesn't change that privitization of radio waves is hostile to everyone but those who can exploit their ownership for profit.
If you exclude MVNOs
>because they're usually entirely dependent on the big four networks (Verizon, AT&T, Sprint, T-Mobile) for voice and a variety of data platforms.
Yes, that's pretty much the definition of an MVNO.
For example, they were the first as far as I can tell to launch extensive WiFi calling and WiFi SMS, even extending to some American airlines (at least for WiFi SMS - calling is possible but socially unaccepted on planes).
Wireless carriers as a general rule are all looking at WiFi offload capabilities especially as 802.11ad and up provide higher transmission rates (peak and average theoreticals).
There is a race to perfect and bring to market seamless WiFi-base station handoffs (both ways) in real-world conditions. I suspect that will require a combination of channel (i.e. mobile devices) + wireless network upgrades, so in the meantime carriers need to bridge the gap. This is arguably a pretty good strategy assuming T-Mobile is expecting WiFi to handle even more of their traffic overtime.