“If we had an actual commander-in-chief, that base would have power.
How?”
Could always move the base, pull out several hundred million dollars in revenue for the local economy and at the same time moving to remove Turkey from NATO. I am sure there are other things out there a CIC with a set of cajones can do.
Move it where? Turkey has allowed a U.S. presence at Incirlik since the 1950's Right now it supports the U.S. strikes against ISIS. You don't just pick up and move something like that even if there was an alternative available, no matter who the commander-in-chief is.
As for having Turkey expelled from NATO, most NATO countries are wondering if the U.S. is going to stay in much less worry about expelling a member.