Forgive my ignorance but what happens during the night when there is no sun? Would the day produce enough to last throughout the night with batteries? Are there enough batteries?
You probably want to diversify into wind too to reduce storage requirements. IIRC wind also produces a bit more power per square meter in Germany than solar. Right now there isn't enough storage to cover the windstill nights, but there are no technical reasons why we can't store the power either in batteries, as Hydrogen or Methane, as heat, or, where geography permits, in pumped hydro (or a combination of different storage technology). It's just a bit expensive right now.
The other factor is that grid storage isn't profitable because there is almost zero demand for it. Please wait until it becomes a problem.