The use of coal is very much a political issue. The social democrats see themselves as the workers party. And historically their strongest base was the coal/steel workers. they have some problems shutting down coal, because this would go against "their own" people (even if there are not many coal worker left). Also some coal mines are in eastern Germany which already faces some unemployment issues and has a lack of industry. But still coal is being phase out. The highest ratio of electricity from coal was 46,9% in 2013. In 2018 it is 38.4%. Not going down fast enough, but still going down.

You are right, that there needs to be some sort of mechanism to stabilize the grid in case renewables are not available. But nuclear energy is not an option for this since it takes days to start a reactor. So what are the options?

* Gas turbines (in the short run, known technologie, fast start-up times, but still creating CO2 even if less than coal)

* Batteries (e.g. https://www.ewe-gasspeicher.de/en/home/b4p )

* Smart Grid (electric cars for example are often flexible in their charging times).

* Pump storage