The US has roughly twice the population density of Finland. Thus it would be roughly half as expensive per subscriber to wire up the US compared to Finland. The key takeaway here is that Finland has shown that it can be done and has been done.
As to whether it should be a should thing or not, it most definitely should be. The regulatory framework already exists for it, it's called the Universal Service Fund. The only thing lacking is that it is not being used for broadband. That needs to change, but as you said there isn't a legal regime mandating that...
In closing, population density isn't the real issue. Otherwise we would not be lamenting that you can't get broadband in California.