Well first of all the scholars have prohibited and most of them say this is not applicable to the western people and also not in non-Muslim majority countries where Muslim family laws are not implemented.
Secondly, that is the failure of those men. Vast majority of them married out of some necessity, either for the same of citizenship/green card/permanent residency or financial reasons etc. Furthermore 99.99% of such men are not practicing and they can mostly be a bad influence on their kids as far as Islam is concerned. I have spent all my life in the west and I know them...many of them drink, most of them rarely pray or tell their wives about Islam...so their children have nothing to associate with them and even less with their culture and religion.
The men I know married these women for "love" (they already had U.S citizenship and were stable financially).
I get your point. Just from my observation, even if the man was practicing and traditional, the children were still influenced a bit more by their mother.