You won't get competition in sparsely populated areas. There's not a ton of business sense to expand and try to compete in these markets.
The alternative way to get build-out in the underserved areas is to have gov subsidize a few interests. Canada seems have done a good job getting cell coverage in the middle of nowhere paying Rogers and Bell/Telus to build in remote lands. The US usually gives build-out requirements for stuff like spectrum and then doesn't enforce them when a company like DISH runs a scam: https://www.forbes.com/sites/fredcampbell/2018/07/20/dish-ne...
DISH btw is in full PR mode lending all their AWS-4 spectrum to AT&T and all their 600mhz to T-Mobile, since they previously didn't do shit with it.
In the case of the landline internet providers, there's around a half-trillion USD tax scam that's been perpetuated since the 1990's: https://www.reddit.com/r/explainlikeimfive/comments/6c5e97/e...
I moved to Berkeley for university and there are several competing options for gigabit internet (including Sonic, LMI, etc.). When the gigabit service arrived to disrupt the AT&T/Comcast duopoly, suddenly the customer was important, and we were able to get great speeds, prices, and customer service.
What I'm saying is that you don't necessarily need to make internet a public utility to improve service, just to get some real competition. If that competition needs to come in the form of municipal fiber, then that might also work, but it could also be a private company.