So, with 5 damane captured, they happen to find one of the five who is as strong as the strongest woman to come to the Tower in the last 1,000 years or more.

You are right about one thing though, I was incorrect in saying they were stronger than the average Aes Sedai. That said, I do not recall seeing a weak damane. Tuon's fortune teller might have been weak, but I'm not sure.

As for why the Tower has the weaker women, think about the practical effects of their restrictions and their pool of recruits.

1. They initiate only women who come to them or cannot be ignored. So, the largest pool of women are from areas where Aes Sedai are kindly looked upon, noble families that see the Power as an asset, and countries/regions like Tear where it is illegal to channel (excluding Amador, where they execute witches).

2. We know that channeling is, at least, in part a genetic trait. Because the Tower has been drawing their initiates from the same pool for so long and not reaching outside of those traditional groups, they have been removing the channeling genes from their populace.

3. The women they do accept rarely reproduce, and so they rarely pass those genes on to future generations in their home region or not.

4. They reject women who have pre-existing ties, ie: married women, women with children, etc. In an agriculturally based society, marrying young is the norm. Egwene was 16 or 17 when the story started, and she was planning on marrying Rand (or becoming Wisdom) soon. Faile, a noble, is married to Perrin at 16 or so, and no one thinks it is odd.

The majority of the women in their world will have formed those pre-existing ties before a representative of the Tower meets them, if one ever does.

5. Women with the spark who begin channeling on their own are looked down upon, are often ostracized if they continue in the Tower, and are firmly dissuaded from even thinking about things of the Power if they are not accepted into the Tower.

We know that women with the Spark tend to be stronger than learners. We also know that women with the Spark will eventually channel, whether or not they come to the Tower. Women who channel before coming to the Tower, especially if they begin learning before arriving at the Tower are called Wilders and lose status in the eyes of the other Aes Sedai. Women who do not join the Tower have it beaten (metaphorically) into their minds that they are not Aes Sedai, that they cannot hope to be an Aes Sedai, and that such ambitions are beyond them... those women likely teach those lessons to their daughters, who might well be learners or sparkers themselves.

All in all, the Tower's system (unintentionally) sets the Tower up to recruit weaker and weaker women as time goes on.