The European countries with lower overall population densities than the US are few: Estonia, Sweden, Finland, Norway, Russia, and Iceland.
In Finland for example according to the coverage maps I'm seeing the northern third of the country has spotty coverage if any from all the carriers. The middle third has 3G along highways and 2G elsewhere. The southern third has 4G most places, but some more rural areas are 3G. The whole country is slightly smaller than Montana. The vast majority of Finland's people live near the Baltic and its gulfs, with 20% living in Helsinki alone. The whole country has fewer than 100 towns and cities and a population density overall of about 18 people per square kilometer over a total land area of 338,424 square kilometers with a total population of under 5,500,000 people.
In 1990 about half of US states were lower than Finland in density, and half were higher. Now only 13 states are of lower density. This is because Finland's population is relatively stable. The US birth and immigration rates are higher. The total density of the US is 35 people per square kilometer.
The twenty-fifth most dense US state is Washington, with about 40.5 people per square kilometer, but in 1990 the 25th most dense was Alabama with only 30.7 people per. Alaska has 0.5 people per square kilometer. New Jersey has 467.2 per. Only 13 states have double the density of Finland or more. Fifteen have less than half.
My current state, Texas, is 696,241 square kilometers holding about 28,000,000 people. 40.8 people live per square kilometer, up from just 25 in 1990. Texas has 254 counties. There are 1,216 incorporated cities, only 246 of which are home to more than 10,000 people. Thirty-five cities are home to more than 100,000, with just six cities over half a million in population. Still, nearly one quarter of the population lives in the Houston metro area. Another quarter lives in the Dallas/Forth Worth metro area. Another quarter live in the San Antonio, El Paso, Laredo, Amarillo, Brownsville, Corpus Christi, and Austin metro areas. That means that one quarter or so of the population is spread sporadically throughout an area twice the size of Finland, with fewer in the deserts in the far west of the state. Like Finland, huge population centers are especially well served by a variety of carriers. Some are as cheap as $30 or $35 a month, like Boost Mobile. The most reliable national carriers that don't drop signal driving across the state on highways among the cattle ranches, forests, farm fields, and such are $50 or more.
When I visit friends and family in more rural areas in Missouri and Illinois, where the largest city or town in any direction for a hundred miles is about 50,000 people and my parents live 7 miles from the closest town (of 900 people) and 8 miles from a town of 16,000, I get consistent 4G at their house. I pay $50 a month. I'm okay with that.
The most recent data from the U.S. Census Bureau (2007) counted 39,044 general purpose local governments, which includes 19,492 municipal governments, 16,519 township governments and 3,033 county governments. It has a total land area around 9,600,000 square kilometers. Yes, it costs money to build and operate in this kind of environment.