Why don't you for once think. Arabia is mostly desert, it could not host anywhere the population of Palestine or any other more temperate area. The number of true Arabs was very small. The "Arab" conquests were conquests by Arabian leaders and converts from Christianity which was the religion of Byzantium. The people of Palestine were all Christians before until after the defeat of the Byzantines at Battle of Yarmouk. There were hardly any Jews and the few Jews that were there were the allies of the Muslims.
I will have to disagree with you. I don't think all those early visitors had problems with their eyesight that they couldn't see that there weren't many people around, mainly Bedouins. Say, if Arabia is mostly desert, why don't they ask the Israeli how to make their desett bloom too?
As for Palestinians and temperate areas, they don't seem to have a problem living in places like Dearborn, Michigan, which I don't think people would consider having a temperate climate. In fact, there are even Muslims living up in Alaska now.
Yes, the people of Egypt and Iraq were probably all populated by the original Christians, and then the Muslims left the Saudi Peninsula and forced them to convert and killed many who refused. Now the descendents of those early Christians who were lucky enough to survive can't even practice their religious beliefs in peace.