I'm vaccinated and I'm German. Your suggestion ignores that vaccinated people are part of the transmission chain exactly as the non-vaccinated. We believed that vaccinated wouldn't transmit it, but they do. Kids too. If you are vaccinated and visit your grandma, you are putting her in risk. Testing everyone and quarantining the positives still our best bet to avoid social conflict while trying to fight this pandemic.
References:
https://www.nature.com/articles/d41586-021-02689-y
https://www.tagesschau.de/inland/innenpolitik/impfdurchbruec... (german)