why didn’t they decide to “phase out coal” instead?

23 years ago, under Schröder they wanted to phase out both and massively subsidize renewables.
Later those plans were largely axed under Merkel.

The reason why coal has a strong standing in Germany is that it is one of the few natural resources the country has.
It has long been a staple in certain political circles to justify coal subsidies by pointing to the many jobs tied to coal mining.
Nevermind that they had no problem throwing jobs in the solar industry under the bus when they cut subsidies for that.