Why would they just let you in because of your family history? I presume your ancestors once left Germany to find a new country to live in and became successful there.
Not saying that Germany shouldn't "let you back in" if you want to immigrate back, but the mere fact that your ancestors were German should not qualify you more (safe for certain exceptional populations in recent war history) than others whose ancestors might for instance come from the UK.
Ah Grandpa (his father immigrated over in 1914) served in the Korean War. Other half of the family was a wave of German farmers to Texas mid civil war and served in the Confederate Army. I am lucky that they are strangely meticulous keepers of family history.
And then your child will forever have trouble opening a bank account, and will have to file and potentially pay taxes for their entire adult life even if they never set foot on US soil again. This "exploit" often isn't worth it, unless the child will 100% certainly live in the US when they grow up.