I think that the biggest problem with having a more extensive area with a "Turkish" language and identity is that historically the Turks started out as steppe peoples, mostly nomadic or semi-nomadic. Generally, when nomads conquered or simply moved into more densely populated civilizations, they tended to gradually mingle with the larger native populations and lose many of the distinctive cultural features that their nomadic ancestors had. Some parts of their language and customs often survive, but they are very mixed with other influences. Meanwhile, the groups that remained nomadic will often spread out over a large area and mix with other nomadic groups, while the language and customs of each local group will diverge over time.
That's more or less what happened to the Turks - various groups of Turks moved into Iran and other parts of the Middle East over several centuries in several waves, and later into India as well. They mostly became Muslim and were heavily influenced by Persian and Arab culture. For example, the Ottoman Empire was considered "Turkish" by Europeans, but its people, culture, and language(s) were actually a diverse mixture of Turkish, Arab, Persian, Greek, and other influences. Meanwhile, the Turkish groups that remained on the steppes mixed with Mongols and other steppe groups, and developed a number of different regional cultures, influenced by neighboring civilizations ranging from Chinese to Russian.
All of this makes it very difficult to keep a unified "Turkish" identity over a very large area for a long period of time. At least, that's how I understand it.
