There is nothing special about Mitochondrial Eve other than the fact that she is our direct descendant through the female line. I'm not sure what the population was back then but we are just as descended from many thousands of women who were alive at the same time it's just that male ancestors will have intervened.

There are a couple of ways of looking at this. On the small scale, we all have four great grandmothers. We have inherited all our mitochondrial DNA from our mother's mother's mother. That doesn't mean we are any less the descendants of our other three great grandmothers from whom we will have inherited more or less the same amount of nuclear DNA.

Another way is to start from the time of Mitochondrial Eve. Of all the women in her generation, some will have only had boys and some will not have had children at all. Their mitochondrial DNA will go extinct. The same happens every generation until only the mitochondrial DNA of one of those women is left. There is nothing to say which of them it would be.