Best Technical Solution The best technical solution is fiber to the home. I don't think anybody can argue against that. The only problem is its financial viability. Corporations want short-term profits rather than long-term investments. The federal government should have stepped up a decade ago and provided a funding mechanism tied directly to fiber deployment for rural areas. Uban areas have multiple companies fighting over them so competition will let them get the best service possible without government involvement.
LTE is not a good technical solution for the long-term and definitely not for the home. It's got a spectrum problem which is just never going to let it expand to a point where everybody can use it at the speeds desired. The telcos only like it because it's relatively cheap to deploy and they can charge based on usage and get revenue on the overage charges.
Fiber is no doubt the best solution. But as you said it is the most expensive one. There are several ftth projects in this area, but funded with federal loans.