There are 3 nation wide 4G networks, every home has old landlines.
What is a true problem however is the political unwillingness to force cell providers to cover areas with very little population.
It is not economically useful to invest in very rural areas, if you would have to invest 2x to go from 95% population coverage to 99% (numbers made up).
The conservative party (CDU) is "business friendly" to the persistent detriment to quality of life of a majority of citizens in a lot of areas.
T-Mobile was part of the Deutsche Post when it was still a government organization and it is still a big shareholder.