Allah clearly knows exactly the best place for Him to raise His Messenger. There are concrete reasons behind the selection of Arabian Peninsula as the place where the last Prophet has been raised. This selection was made in accordance to His knowledge. One of the reasons is the Ibrahim's (a.s.) prayer to Allah.
Ibrahim's Prayer to Allah
The selection of Arabian Peninsula was made due to Prophet Ibrahim's prayer to Allah. His prayer is quoted in Surah al-Baqarah, verse 129:
رَبَّنَا وَابْعَثْ فِيهِمْ رَسُولاً مِّنْهُمْ يَتْلُو عَلَيْهِمْ آيَاتِكَ وَيُعَلِّمُهُمُ الْكِتَابَ وَالْحِكْمَة وَيُزَكِّيهِمْ إِنَّكَ أَنتَ العَزِيزُ الحَكِيمُ
"Our Lord, and send among them a messenger from themselves who will recite to them Your verses and teach them the Book and wisdom and purify them. Indeed, You are the Exalted in Might, the Wise."
In this verse, Ibrahim prayed to Allah for raising up a Prophet from the Arabs. So, Allah granted his prayer. Every prayer comprises two components: (1) time and (2) nature. Prophet Ibrahim did not mention a specific time in his prayer but normally people will pray for an outcome in the near future. But, Allah modified it for two thousand years later when He finally raised Prophet Muhammad SAW in Arabian Peninsula.
The place for raising up the last Prophet was not just randomly chosen. There are concrete reasons behind its selection. Allah The- All- Knowing has made the best selection to raise His Last Messenger as the Mercy to humankind.
Reflections on the Prophetic History, 2014. (IIUM)