Now this actually sounds pretty cool and exciting. I wish there was a Christian equivalent that I could go on, although preferably one that would be allowed any time of year.
Christianity has it a bit rough on that front. Its holy cities like Jerusalem, Bethlehem, Nazareth, and Antioch aren't exactly in friendly hands, and Rome and Constantinople are only holy cities to certain subsets of Christians.
One of the most critical developments towards the creation of the Papacy was the shift in the balance from "Five patriarchs representing holy cities of the Pentarchy" to "Oh s**t, Jerusalem, Alexandria, and Antioch are in enemy hands, guess we're down to just two," in dramatically accelerating the concentration of power in Rome. Once Rome and Constantinople fell out with each other, that finished the job.
Anyway, the Hajj is a fantastic idea marred by some horrible infrastructure nightmares. It is pretty much expected that a few people will be trampled to death every year.
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