I think most people avoid it not because of the children or the expenses. But rather, the ex of the woman is constantly meddling in their private life.
It also depends on how the woman got single after having kids. I mean, you've got to be in a serious relationship in the first place to have kids. If she is a widow, most people won't mind. But if it is because her previous partner was a jerk, then it also raises questions about her own maturity and decision-making. Why would she have kids with someone that irresponsible.
So, to avoid all that, I agree to some degree that people with kids should look for people with kids. So that they would be on the same level as their partner.