Noting the fact that most women spend about 20 years as novices and accepted, giving them the time they need to grow to their full power, to me, there must be a reason for that situation.

It cannot take most women 20 years to learn everything they need to know about the Tower and the World. Siuan, Moiraine, and Elaida all did it in six years total, and they come from wildly varying backgrounds. One a fisherman's daughter, one the niece of a King, the other a minor noble. If just Moiraine and Elaida progressed that quickly, we could chalk it up to their superior education as nobility in all things political, historical, etc. But because Siuan also progressed just as rapidly, it shows that a woman can achieve all the skill and knowledge needed in less than a single decade, not the average of two.

So, again, looking for a reason, I thought about what changes for a woman over that decade or more during which she is supposedly still learning. The only thing I could pinpoint is her strength in the Power. We're told that women achieve their strength in a linear scale over time. We were also told that Moiraine and Siuan were no where near their full potential when they were raised. From that, we can extrapolate that most women will not be anywhere near their full potential when they have been studying for six years at the normal pace of the Tower.

So why not let them grow into their strength as Aes Sedai, like Siuan and Moiraine, and Elaida for that matter, did?

Because Aes Sedai play the game among themselves. Aes Sedai know who they can order about, whom they must listen to, and to whom they must bow, and they base that entire system on strength in the Power.

Now, say you raise a woman like Moiraine who is one of the strongest of her generation, who learned faster than any woman before her, but raise her when she is at half of her full potential. Stronger women will insist that she obey them, knowing full well she will outrank them within years, and your strong, young Aes Sedai will see that Strength is a horrible means of judging who should lead.

If she is brought in at her final position, that will be all she knows. If she is brought in while at 1/2 potential, she will see her opinions gain more weight, see as people re-evaluate her, based solely on an inborn characteristic.

Someone who is opinionated, and not afraid to share it, could easily overset the whole process by calling attention to the fact that they treat wise, capable women as little more than servants simply because of their relative weakness.

The base fear would be introducing uncertainty into the system. These women will grow and change their positions while still Aes Sedai, which could lead to other changes, and change is bad (per normal Aes Sedai thinking).