This is exactly what I'm talking about. CenturyLink is the result of consolidating RBOCs (like US West/Qwest, Wisconsin Bell) and ILECs (like Centel, Pacific Telecom, Sprint/Embarq) and is one of really just 3 ILEC/RBOCs left (AT&T and Verizon being the others). These are the companies that run just about all the PSTN (Public Switched Telephone Network) that is the traditional physical copper telephone circuits around the country. They operate under an FCC mandate that goes back several decades that every address can get a dial tone (which you pay for currently as the Universal Service Fee). But that's only a copper analog telephone, not telecommunication services like cell phones or Internet. Those are not (yet anyway) regulated to be common carrier monopolies like AT&T and Bell were.
At least half of American households dropped a landline altogether and something like 75% of businesses have gone VoIP. Last I saw it was 3% of users still using dial-up and those 3% make up a tiny fraction of the revenue generated by Internet access. So there's zero incentive for CentryLink to spend one dime maintaining the infrastructure and they are pretty much just farming the existing landline customers to bolster their IP operations at Level 3 and Savvis. I doubt they care beyond keeping the number of FCC complaints below some threshold. Even the FCC really couldn't care less about PSTN customers as long as no Congressman gets a wild hair I suppose.
I have no idea why Hughes wouldn't want to sell you access, but they are a pretty big satellite Internet provider, well over a million mainly rural customers. They do augment with LTE so perhaps they think since you already potentially have access that way that they couldn't compete against a cell phone company in your area. A 4G/LTE hotspot is going to be pretty similar in speed and data capacity and eventual throttling.
There are other satellite Internet companies, Wildblue (Viasat) for example. Or perhaps there's a fixed microwave wireless company in your area. Those tend to be small companies that provide service to a geographic location that otherwise has none.