Since the problem is lack of internet infrastructure, as the market has failed in providing decent internet to a significant portion of the population, I suggest that the government subsides (or even funds) the infrastructure projects required for bringing the portion of the population a decent internet connection that the marked has failed.
That seems like a pretty obvious policy change that a mere layperson can come up with in their couch. I’m sure a civil engineer can do better though.
I don't know how much you can say it's a market problem as such, a role is clearly played by regulatory capture combined with/leading to/reinforcing monopolies. Local american governments granting big ISPs de jure or de facto sole rights to law down cable in a town means it's very hard to break in to the market as a hypothetical newer, smaller ISP.
I don't know that monopolies and rent-seeking wouldn't show up anyway with laxer regulation, but it's something to be taken into account.
Like I indicated, I’m not a civil engineer and am in no position to be coming up with a policy my self. I can say though—and I might be wrong—that America has some policy that might be hindering traditional infrastructure being build to provide decent internet connectivity to some parts of the population. I’m sure there are civil engineers though that can provide examples of better policy that may help solve this issue.
Claiming that the market has failed in a industry that has been utterly dominated by government and that was never actually a real market is pretty rich. This started out as basically a state monopoly that was then partially privatized but local monopoly laws were held in place.
Just throwing more money at utterly gridlocked system is not the solution.
So all you need to do is change the policy determining billions of dollars of infrastructure and profits with powerful entrenched interests? Where do I sign up?