Sometimes people can be committed to helping each other but are not exactly competent. This can be a problem too.
Spirituality comes in , becasue people that go to church tend to spend at least a little time in self inspection. They are open to the fact that there might be issues in their life that need correcting. So people that go to church and are spiritual tend to also be more reponsible.
In summary, marriage needs both people to be committed to the interests of others in the family, marriage needs competence, and these things generally don't happen without spirituality.
You are, of course, absolutly correct in your observations. If God (IMO) is not the REAL head of the household (from BOTH spouses POV), then the relationship is probably doomed. Only one spouse believing and trying to do right to maintain the "marriage" will usually fail.