The reason is actually quite simple when talking specifically about Anatolia. The High Plains of Anatolia were like a little steppe that somehow splintered of the main steppe. The Turks who are people from the steppe did not only militarly defeat the Byzantian, they went raiding in Anatolia and discovered a area that was very habitable for them.

They established themselves there, not just for raiding, but to live the traditional steppe lifestyle. Its a very common pattern that Steppe Societies establish trade relationships with the Settled Societies as they can both benefit quite a lot, the reason is that the products the two societies produce are very different and thus very useful for trade.

The Byzantians saw this as a huge problem but never managed the get a handle on it. They tried to defeat them militarly, and hopefully establish some control and regulation over them. They did not want indpendently organised 'kingdoms' in Anatolia. That never worked because people of the Steppe tend to have a advantage on home turf and the logistics were quite difficulte.

They tried to make the Turks Christian, a strategy that was right out of the Byzantian playbook. The problem was that the Turks were already Muslim and so they could not be converted the same way they did the Slavs.

Another very important reasons why this area is so Turkish, and not so Greek today. Because of the weakness of Byzantian the Eastern Chritian Church , they did not have the money needed to keep up all its commitments. The areas under Turkish rule saw less and less of the church and and more and more of islam. A slow process then of conversion then took place over a long period of time.