This is a common misconception. The yellow bin (Gelbe Tonne) is not about recycling at all. The point is that, in Germany, producers of packaging need to pay a fee per packaging that goes towards disposing of the used packaging, through the Green Dot (Grüner Punkt) system. The yellow bin is therefore paid by them, as opposed to by consumers.
This is why the yellow bin is not being described as accepting specific materials, it's explicitly described as accepting packaging (both plastic and paper/carton).
When you put a non-packaging plastic item into the yellow bin, it counts as an "intelligent misthrow" (intelligenter Fehlwurf), which is one of my favorite pieces of jargon.
That will increase the cost by an unignorable margin and even that, some biodegradable plastics still take a long time (a year or even years) to be gradated.
This is the reason of why things like reusable plates etc is currently the best way to go. That is, when those reusable items actually gets returned.