Every map I've seen of the Ottoman Empire has it hugging the coasts of the Arabian Peninsula. The former Caliphates were all able to take the entire peninsula. Was there a reason the Ottomans didn't do the same?
The simple answer is that there really wasnt anything to conquer in the rest of the Peninsula. To the west, Ottoman Empire already controlled the holy cities of Mecca and Medina, hugging the Western coast. To the East, Ottomans controlled Basra and Mesopotamian region, establishing a strong control over the trade from Asia in to Europe without needing to take Oman. Otherwise, the Arabian peninsula is essentially desert, little of value. Instead the Ottomans were contending with Europeans and Persians, both of which were much more desirable targets than sand.
TL;DR - Not worth it.
