First, the Tower's reputation. Unless a girl spontaneously starts throwing fireballs, most people wouldn't want to send one of their own off to that Tower.

Second, Aes Sedai don't do much recruiting. Partially because there's so much ground to cover, partially because, well, they're too busy doing other things. Verin and Alanna's trip to the Two Rivers seems to be the exception- most Aes Sedai just pick up recruits incidentally, as they're doing other tasks.

Third, which is more of a combination of the first two, Randland is the only- the ONLY- place where testing for the ability isn't mandatory. The Sea Folk, Seancean, Aiel, and Sharans ALL test for it.

Finally, and I'm not sure how much this affects things, but other countries don't discourage their channeling women from breeding. I don't know if the Seancean breed their damane (it would seem completely in character for them, though it's mentioned that men who sleep with damane are considered perverts), but it seems like the sul'dam can marry. Wise Ones and Windfinders can, certainly. The BWB says Shara has an odd system, but they do make sure the ability isn't culled out.

Aes Sedai, on the other hand, are aloof, raised away from men, and generally don't get romantically entangled with them. A few thousand years of that surely had an effect, no?