Basically, if the US bases go, the capabilities of much of the European military forces go bye-bye. They're optimized for using American logistical support, (because they have no reason to develop their own) and all of that comes through American bases in the region. I'm sure that some political parties in Europe would be completely okay with losing that capability, but most people agree that there is one thing worse than a strong military, and that's a weak military that costs the same amount of money as a strong military.