A ssome else pinted out, by funding public braodcasting directly they can afford to be critical. Were the fundid by a tax, collected by the gevernment, and handed out by the government this independance goes right out of the window. One of the lessons Germany learned from the Nazi regime with government controlled media.
In Germany, the government has no direct control about the TV fees. There is a complex mechanism for deciding about increases, which involves independent entities. Especially, the government can't just cut the fees to influence the media.
In order to increase the fee for public braodcasters, not a tax (small bt crucial difference), both chambers of parliament have to agree. The bundestag is directly elected, the bundesrat represents the indivdual states. This means, in order to change the fee, every state and the bundestag have to agree. For the states, that means one single state not voting for a fee change prevent any fee change. Just happened, one state government feared backlash from the AfD and the right wing from the CDU (Merkels party) and voted against an increase.
So in order to change the fee, it is not just one govnment that can do something, but a grand total of 17 (federal plus 16 states). Usually they all agreed, but with different ruling coalitions in each state, this mix of left and right having to agree in itself prevents the public bradcasters from becoming a tool for government propaganda. They do represent the establishment, so. Populists hate this.
EDIT: To be really accurate, the legislative branch sets the fees, not the executive on. The legislative consists of two houses, Bundestag and Bundesrat. The Bundesrat is controlled by the state governments, which are composed of local arms of the parties present in the Bundestag (kind of like congress) and regional parties, mostly those state and federal governments are coalitions of multiple parties. It is the party line thing where it gets blurred between executive and legislative bodies.
EDIT: I fell for a common misconception, as an other user pointed out. It s not the Bundestag and Bundesrat deciding these fees, but rather a compact of the 16 states. The same states make up the Bundesrat, the compact is not the same body, so. Which further decreases the influence the federal executive, and even legaslative, branches have o public broadcasting.