Is it worth paying 40k a year for an Ivy League level education if you can study for free in your home country?

Really depends on your objective. If you want to be a mechanical engineer, get your basics covered in Germany for free. If you later decide to do something revolutionary, you’ll join a specific program or firm and perhaps that brings you to the US.
 
The basics of classical engineering programs are very similar internationally.
 
If you are interested in Mechanical Engineering because you already know you plan to build ground-breaking, revolutionary new things, the resources at a top US school are hard to beat.