It seems the most stupid thing ever that Robotnik would ban all music, right? But this is Truth in Television in some dictatorship countries, where the only music and entertainment allowed is strictly government regulated and all based on pro-government propaganda. Take North Korea for an example. Robotnik took it to its logical extreme because he doesn't like any music. It has three uses for the closed-fist dictator:
It shows the people just how much power you have over even the smallest things in their lives.
It is a simple way to root out people who are uncomfortable with your strict laws - if somebody's playing unauthorised music, a stupid law yet very easy to obey, they wish to rebel against your rule.
Music is an easy way to express your feelings, send messages, and inspire hope in many people. Not something you want the people of a dictatorship doing too much.
