No - I never got the feeling that anyone selected the slayers. My read is:
Way back a two part spell was cast.
Part1) - tapped into the power of dark magic to given superpowers to certain girls to fight vampires other demons.
Part 2) limited that power to 1 girl at a time - otherwise every girl with those characteristics would have gotten the power.
My feeling is that part of the selection process for part I was that they would tend to use that power for fighting demons - that most of them would not use it selfishly. Because of the whole "free will" deal there was not guarantee - but that they loaded the dice that way as much as possilbe.
And so when Willow the White got involved - she either just cast part I, but not part II, or since the actual word "recast" was use, recast Part I while repealing part II. (Part I was still Black magic though - so her becoming Willow the White is an argument for her simply repealing part II.)
And I realize that this has absolutely nothing to do with Cindy's point, which is quite correct. It is just a side-note her post sparked that interests me.