TK did run extra flights from STN to IST in the run up to Christmas last year in Turkish Airlines livieried AC.
I suspect that at the moment they don't want to serve the two airports from STN, as many people will just chose the cheaper SAW flights, unless going to IST for the connections.
There is talk of Anadolu Jet being seperated from Turkish so I don't think that we will see IST and SAW served from STN until that happens.