Totally makes sense. If she is a widow - then that's different. Or if she was married to the father of her children (and only had children by that one man) and they divorced - then that is also OK, depending on why they divorced. But what sane man would date a woman with 5 kids by multiple guys?
Accidents happen, and if she has one kid by one guy and is doing an amazing job raising that child, is not bitter, is able to support the child... OK, that is also a different situation.
But emotionally mature women look for good guys to be with. If a woman is interested in the type of guy who has many "baby mommas" then she may have emotional issues that would make her a bad partner.
BTW, none of this absolves a man from being a responsible adult, either. Which means - he should also take equal responsibility for using birth control if he is having sex outside of marriage and he should take responsibility for any children he does have. Using women for one-night stands when they are looking for a relationship is not ethical, nor is walking out on your kids. Of course, if the woman also wants a one-night stand - no harm, no foul, just make sure you also use birth control, even if she says she is on the pill. I've had guy friends who trusted the woman when she said she was using birth control and then ended up supporting a child.
(Another comment on here pointed some of this out. And it's only fair - if you want a responsible woman, you gotta be a responsible man.)