I believe there is no Federal requirement that there be a Provider of Last Resort (POLR). State law might require it, but in at least some states there is possible to have areas without a POLR. At the national level the regulatory theory is that when there is sufficient competition in a market, the POLR requirement is relieved. In any case, POLR refers only to phone service, not Internet.
Where I live, you can get AT&T POTS from the ILEC of record. Sometimes it even works...when their cross box/remote terminal isn't full of water, has power/batteries haven't died, etc.! They really push people toward their "wireless home phone" solution which is basically an LTE radio and ATA in a box. It's somewhat significantly cheaper than their wireline POTS service.
No DSL, no HFC/cable, no consumer fiber. T1 is available at full tariff rate from the 90s plus about 20 miles of line extension charges. ISDN is no longer offered (or so they say).
Only wISP worth mentioning (i.e. can deliver more than 1Mbps on a good day) is myself (fiber coming this summer hopefully). Basically the entire township is a dead zone as far as wireline goes. I pay dearly for my dedicated fiber backhaul to make service worth using available.
I'm about 10 minutes from the county seat which has population over 10k and about 45 minutes from downtown metro of >800k. Most gov. agencies have the entire county flagged as "not rural" and ineligible for subsidies. These areas definitely exist.