Speaking as the bright red spot in the middle of yellow and white...
It's easy to say that we should just pour money into buildling out the fiber network. However, there are some key things not already touched on. While it is true that there are vast stretches of the US that contain few residences and more cattle than people, I believe well over half of the US population actually does live within a close distance of a major city. Case in point, my state of Minnesota has a population of 5.2 million, giving it a density of 65 people per square mile (25 per sq km, for everyone else). However, the "metro area" of Minneapolis/St. Paul has 3.2 million people in it and only has about 1/10th of the state's land, which means that the other 71,000 sq miles has 2 million people. That area has 10 times the size and only 3/5th the number of people. And even in those areas, there are mini-cities that act as the urban area. So there are islands of population, with not much in between. For those in between areas, it's too expensive and a poor use of resources to spend all that time and money. Mobile phone coverage is only now getting to near saturation of digital bands, and those have been growing since the 80s. It's just a fact of life that if you chose to live in the middle of nowhere, you can't expect the same level of service. In some places, a township (land that isn't part of an incorporated city) contracts to cities, counties, or even the state to provide basic service such as police, fire, and emergency. In some cases, it's up to each landowner to contract out for the services, and to pay for build-outs of power, water, sewer, and paved roads to their land. Otherwise, you drill a well, have a gravel road, drain into a septic tank, and install solar and wind turbines to fill your power needs.
I know it's hard for even those in the densely populated parts of the US, let alone the very densely populated EU contries, that there are people who choose to be off the grid, and probably wouldn't use the services even if built to them. There are really no incentives for a multi-million broadband build out to some township of 15 houses and farms, when only two will actually use it, until they get the first bill.