It is ultimately the wisdom and decision of local govt. to allow a military base or not. But one things is for sure that Turkey is not a stable country. A country which cannot protect its citizens and where a big minority is at war with state cannot assure security to others. Military in Turkey have intervened a no. of times and toppled govts. Erdogan had a close shave recently. It is a different matter that he himself is no better than a dictator.
With American base already here, I dont think that this country needs any other base. Even if it wants, they should opt for some other country.
But then again govt. knows better how to defend the country and is the best decision maker.