Is it odd they are going after SpaceX? The funding they received was earmarked to support unserved census blocks. If any company is in a position to help unserved rural areas it is SpaceX, no?
I'm not sure any contact or such is 'going after'.
Not really - it is very unlikely that SpaceX will be able to cost-effectively serve high-speed internet for any interesting amount of people in a relatively small geographic area, such as the United States, as at any one time only a very small number of satellites can serve a particular area. This becomes especially problematic with any realistically achievable size of the constellation, which is going to be much closer to the current size (~1700 satellites) than to the "promised" size (~42k satellites).
Laying cable seems much more achievable and maintainable than launching 42k satellites every 2-5 years as Elon is "promising" (remember that the maximum life span of any satellite in LEO, as mentioned by SpaceX, is 5 years, after which it will de-orbit naturally).
I'm sure Starship will fly in a few years and carry more satellites at a better cost per ton than existing rockets, but there is no reason at all to believe anything close to the announced timelines, sizes, and costs. At any cost per launch per ton that is even somewhat comparable to any existing rocket (say half of), 42k satellites is far too expensive.