Why didn’t Ottoman empire control whole Arabian peninsula?

It wasn’t worth it.

The South-eastern part of the peninsula was inhabited by Arabs allied to the Turks, so no need for conquest.

The Empire controlled the more densely inhabited areas of the West and East which were the largest trading establishments, included the holy islamic cities of Mecca and Medina and also much of the coastline and ports. Stationing troops in the middle of the desert to guard sand wasn’t really a good investment move. Had they attempted to do that, they would have succeeded but they would have to defend against raids from indomitable bedouin tribes which would drain manpower and resources best used elsewhere. Oil wasn’t a big thing back then.

Instead the Ottomans traded with the bedouins coming and going to and fro. This way they got what the land had to offer without expending themselves.

Christos Terzis