I think the solution is what the developing countries have done: the national government just install the cables, then rent out the infrastructure to private companies to compete/service.
Several cities in the United States have implemented municipal fiber. There are a few different models [1] but my favorite is "open access", where the city owns the fiber and allows many providers to use it. (See more here [2].)
UTOPIA, a consortium of cities in Utah, operates under an open access model. You pay a $30 fee to the city for the line and then choose from 12 different ISPs [3]. A symmetrical 1Gbps plan is around $50, so $80 total. You can even get a 10Gbps plan for $200. If you're having problems with the ISP you're using, you just go online and change it.
Utah is one of those states that has laws that were originally crafted to prevent municipalities from providing the service by big ISP lobbyists. The law prevents municipalities from offering the service directly to consumers (still does), so UTOPIA was born with an open access network via a 'loophole' if you will in the laws.
I think the government involvement should be minimal. They should create a law that requires bidding on local infrastructure, and enforce that the bidding process is fair, and the selection/voting process is fair.
In telecommunications redlining is used to carve out profitable areas to serve and abandoning others.
It doesn't matter how fair the bidding and/or selection process is, you'll only end up with service in the profitable areas anyways. The bidding winner will most likely in most places be the incumbent, since they have a leg up.
A similar concept is gerrymandering where you manipulate district boundaries to get the desired election results.
The issue is profitability (similar to the post office problem) -- if your house is in a rural area with low density, it's not worth it for a private industry actor to bid on your linkage. In many parts of the US, the only ways to get mail is through USPS (FedEx & UPS just don't service unprofitable routes). However I think internet access is a human right and a public good no matter where you live or can afford to live (imagine raising children who would never have access to at least broadband-level speed -- how would they function in a 21st century economy?) - and the infrastructure can only be provided equitably if the government steps in and subsidizes away the profitability problem.
UTOPIA, a consortium of cities in Utah, operates under an open access model. You pay a $30 fee to the city for the line and then choose from 12 different ISPs [3]. A symmetrical 1Gbps plan is around $50, so $80 total. You can even get a 10Gbps plan for $200. If you're having problems with the ISP you're using, you just go online and change it.
[1] https://muninetworks.org/sites/www.muninetworks.org/files/20... [2] https://muninetworks.org/content/open-access [3] https://www.utopiafiber.com/residential3pricing/