My issue isn't with the geopolitical reality of an Anatolian state--I agree that either Byzantium controls all of Anatolia or it controls none of it. My problem is with people that wank the Byzantines in an unrealistic way.
IMO the Byzantines were prevented from Ottoman-like expansion for two reasons: the fragility of their government and their compatibility with the geopolitical realities of the Middle East. The Byzantines were permanently cursed with instability--civil wars were always possible and they were always surrounded by nations that wanted to take territory or conquer them outright, so any sign of weakness allowed foreign incursions a chance to succeed. In addition, by my understanding by the 11th century the nation had begun to decentralize under magnates, which further destabilized the country--correct me if I'm wrong.
As for the compatibility idea, to put it simply no one in, say, Egypt wanted to be ruled by the Byzantines, and the Byzantines would not have (IMO) tolerated or been able to maintain the type of autonomy that would have pacified the rebellious groups. All of the non-Orthodox Christians in the Middle East (Miaphysites, Nestorians, etc.) disliked the Byzantines and in some cases preferred the Muslims as rulers. In addition, while the Byzantines sometimes tolerated Muslims in the empire they didn't tolerate heretics if they could help it, so there would probably be purges and/or forced conversions if the Byzantines took lands with heretics. The Byzantines would not win the hearts and minds of areas that were not Orthodox, and couldn't even draw on the legitimacy of the Caliphate as the Ottomans could. If the Byzantines set up, say, a more autonomous Exarchate of Egypt to pacify Egyptians, it would almost certainly break free as soon as the next civil war broke out.
In other words, a post-Fourth Crusade PoD would at best allow Byzantium to reconquer Anatolia and possibly parts of Syria and Lebanon. Beyond that I have my doubts.