By default the Gift is only one in every 10k people. That is only about 6,000 alive in all of Mystic Europe (plus any in the outer Tribunals). While the Order is only about 20% of that total, there is a lot of competition for Gifted individuals with the varies hedge traditions and also a large percentage of loss which are not found until they are to old to apprentice (if found at all).
If we are looking at just the people in the age range acceptable to be apprenticed, there is a total of only about 1,200 of them in Mystic Europe. This means that at any given time there is only roughly one child in the age range to become an apprentice for every Hermetic Magus. And even then, some of them will be older than what a Magus would want or younger than 5.
In an older thread I did the math on how far and wide you would have to search to find someone with the Gift, as well as how far you would have to search to find someone in the age range to become an apprentice. They were massive enough that if the Order did not form groups who systematically searched out those with the Gift and age range required, they would have already become larger in size than could be supported.
I will try to dig up the thread and link it in this post since it does a better job of the breakdown.
EDIT Found it, this is my first post on the subject though you might have to backtrack a touch to find all of it.