That's how cutting edge research is organized. Surely no one in the US believes sending their kid to Harvard for a bachelor means any of the work done by PhD candidates somehow majorly transcends onto them?
The research absolutely impacts teaching to a great extent. We are only humans after all, and I don't have a separate brain for teaching and for research. If you separate your best researchers in research institutes, you're going to seriously limit the flow of knowledge to your bachelor and master students. And those students are your future researchers.