There are two broad reasons why the US has troops in Germany (and in Europe overall).

1. Because the Europeans wanted them there. NATO was a big security blanket, and certainly since the end of the cold war, up to say... 2014, America -wanted- a compliant Europe.

2. Because Europe is an amazing springboard into the middle east, and America just can't help but get itself involved in dropping bombs on the middle east.

1 ties into 2. A compliant Europe is less likely to raise objections to being used as a forward base for bombing Iraqis and Iranians. It's only in the last 10-15 years that the US realized that perhaps it was/had squandered it's lead to China, and dropped the ball (Europe at fault too) on properly containing (or addressing) Russia, and it would sure be nice if it could focus on the Pacific.