Don't be afraid to rent a car.
I would basically agree, but also don't believe the myth that driving in Europe is no more difficult for an American than driving in the US. Traffic signs in Europe are different than what we are used to in the US. Get a copy of international symbols and learn them. Know the difference, for example, between the signs for a passing zone and for a no passing zone. It could be worth your life.
Unfortunately, not all traffic information is by internationally recognized signs. I was once riding a bus in Germany when we came to an intersection, and there was a big sign there giving, in German, special instructions for using the intersection. I can imagine some American driver, who didn't understand German, sitting at the intersection, with honking cars backed up behind him while he tries to find a translation of the intersection instructions on his iPhone.
And don't be afraid to use public transportation.
Public transportation in Gemany is very efficient. Germany has the most extensive rail network in Europe, and it is augmented by a very dense system of buses. I've spent ~150 nights in Germany, 85% which were in small towns with less the 40,000 population, and never needed a car to get to where I wanted to go. It might take a little effort to learn to use train schedules on the German Bahn website, but it is really not much different from using plane schedules over here. And, although a trip by rail might entail more changes than a trip by air, changes in a train station are far less difficult than at an airport.
I think Americans tend to shy away from using public transportation in Germany because we don't have an effective system in the US and are unfamiliar with how one works, but try it. In the US you have to have a car to travel, but Europe is not like the US. It will be a new and fun experience to use effective public transportation, and don't we go to Europe for the unique experiences if offers. Public transportation in Europe is cost effective. For most of my recent trips to Europe, I have priced out my transportation using public means vs a rental car, and a rental car has always shown itself to be far more expensive.