In response to your question, have another question. Does a man having a child with woman mean she won't have other children? I don't see any reason it does.

Would a man having a child with 10 women cause huge social problem? It certainly does. Do you want to be a single woman with kids? Doubt it.

Why should men get special status over women with the number of children they have? I really don't see any reason for that. There are men who deliberately get women pregnant and then leave them because they think they are great and winning life because they have so many children and let other people care for them. Those sort of people would support only having limits applied to women.