Ugh, not this thing again, Ottomans=/=Turkey.
The Ottoman dynasty was heavily Greek influenced and saw itself as the Islamic successor to the Roman Empire. They even had their own version of Turkish full of Persian and Arabic loanwords, they filled their bureaucracy with Persian speaking foreigners. They were not a Turkish nation state. Rum might fit that role better, but even Rum was primarily influenced by the Persian culture.
CK2-wise, Ottomans at the beginning start with the Kingdom of Anatolia/Turkey/Rum/etc, later they claim the Roman throne. IMHO this aspect is represented very well by the Emperor tier upgrade. The important thing is -- because this is the point -- that the Anatolian minors shouldn't be able to form the Ottomans and Ottomans are no longer Ottomans when the Bayezid dynasty succeeds to the throne. Therefore the gameplay mechanic change I've suggested in the previous post.