Both sentences are debatable. Regarding the first sentence, it's possible that the optimal firm count in some communities and especially sparsely populated areas is one (i.e. an actual natural monopoly), but in most communities I would expect it top be at least two or three, since broadband can be delivered through phone lines and cable television lines (which most communities are wired for). There are obviously other feasible media, like power lines and wireless. Could you explain why you believe that last-mile infrastructure is inevitably a monopoly?
Regarding the second sentence, it's debatable that government control is a good solution even in situations where the optimal firm count is one. An ideal government solution may be better than the average private solution, but likewise the ideal private solution may be better than the average government solution. We ought to compare the average case for both solutions, which is to say, the actual outcome we can reasonably expect to get given our specific inputs (our system of government, existing infrastructure, market demand, etc.). I won't claim to have any convincing evidence either way, but I'm not so confident that a government solution is obviously going to be better than a private solution, even in a true natural monopoly.