There are places for Germans to save but they really dislike investments or any type of risk. Sure, Germany could borrow more and issue bonds but I doubt this would change yields for those bonds so much that investing in them is worth it for retail investors. The demand by institutional investors (insurances, pension funds) easily outweigh retail demand.

Also, how would Germany invest in infrastructure if order books at construction companies are filled 1-2 years in advance? If anything, they'd fuel inflation and price out private investment.