Rathauses make empire maintenance cheaper, allowing for a faster expansion rate. Building Courthouses in every city cuts city maintenance in half - Rathauses cut that number in half again. That's great for securing more resources, especially with Charlemagne's cheap Settlers, or going to battle with his war-focused traits.
One issue, however, is unlike the other Courthouse replacements, Rathauses are still as expensive as normal Courthouses. And since Charlemagne isn't an Organized leader, the cost is quite immense in low-production areas. As such, Rathauses do best in the later game, where plenty of production bonuses help build them up at a reasonable rate.
In German towns and cities the Rathaus was a central location used primarily for town council meetings and other official business. It was also used as a large meeting space for interest groups as well as for other activities, depending on the town's policies.
Germany has several famous rathauses, including the Rathaus Schöneberg. The Rathaus Schöneberg was built in the Berlin borough of Tempelhof-Schöneberg between 1911 and 1914 before Schöneberg was absorbed by Berlin. After World War II, the Rathaus Schöneberg served as the temporary seat of government for West Berlin. Upon the destruction of the Berlin wall in 1989 the Rathaus reverted once again to its original function as City Hall of Schöneberg.