The above represents my opinion, and mine only, in the subject of men dating or marrying single mothers. I think that I should be best served holding out for a childless woman and starting my own family. Biological fatherhood is difficult enough; I don't need my life complicated by having to deal with someone else's child.
Still another important factor is the role of the biological father of the child in the lives of the child and of the mother. As the biological father of the child his right to have a hand in his child's life is inalienable. He may object to my way of disciplining his child and in such a case, if the mother sides with him, I would immediately end the relationship as an unnecessary complication of my life. Besides, his right to a hand in his child's life would negatively impact my own intimate time with the mother and of course my relationship with the child, because he may wish to visit his child at a time inconvenient to me and even to the mother. If she's not really over him, my life will be that much more complicated. If he wishes to co-parent the child, I cannot meddle in this and would feel that much less relevant to the mother. This is a dynamic I don't think I have what it takes to be part of.
Next, there are certain complications common to such relationships that I don't think I need in my personal life. Some of these single mothers seek men in their lives to be providers and fathers to their children. If I am to provide for you and be a father to your son or daughter, I think that part of the package should be the administering of needed discipline. From this comes much of the conflict between partners in relationships like these: I am not the child's father and both the child and the mother are likely to remind me of that, and not necessarily nicely. Obviously this is something I would view as unfair to me.
First up, I would want to work hard and expend myself to provide only for my own biological kids. I think that this is natural for any man and I am no exception. Dealing with someone else's child can quickly become a thankless job in a society in which fathers and stepfathers are often viewed as unnecessary and treated with little respect.
I have seen single mothers these days seeking dates with men. While I respect them and find nothing wrong with their looking for romance, I would not date one.