Actually, they did. The first Crusade attacked and took Jerusalem because of that. Much of it was launched at the request of the Eastern Roman Empire, but disagreements between the Emperor and the Crusaders led to separate kindoms instead of winning back the Holy Land for the Romans.
The 4th Century developed a bunch of historical "relics" and pilgrimage sites in the Holy lands. Contantinius Magnus sent his mother, with some court officials to research it and decide on the "right" locations.
Pilgrimage was their tourism. Like tourism, it is tremendously lucrative, and businessmen can charge Capital prices for trips to the provinces and back country swamps.
One major advantage that Islam had over Christianity was the more central position of pilgrimage in its pseudo-theology.
The second major advantage that Islam has is, being invented by an aspiring caravan raider and pedophile, it has plenty of exceptions to any moral precept. The exceptions are calibrated to allow any pirate, bandit, or robber to do what ever he wants, so long as he pays his skim. Very convenient.
Oh. I need to study up on that.