For that reason, marriage became a secular contract between two people and the government.
It is that last part that makes me bristle. It is like two people are in essence, marrying each other and the government. I know couples don't see it this way but that wording does suggest it.
People can still "get married" without the government. The rise of cohabiting couples who have children and pretty much carry on in every way as if they are married minus the marriage license is proof of that. Two people can commit to each other in "marriage" without any religious or secular ceremonies. Two people can decide to have a ceremony in either a religious or a secular context.
The rest is just property and legal obligations that the partners agree to privately and that can easily be handled under a separate legally binding contract similar to a business partnership. In case of a later contract dispute, that can be handled in civil court just as other contract disputes are handled now. For those who think that drawing up contracts detract from romantic view of marriage, a simple template that simply says something like upon dissolving of the contract (ie divorce) joint assets are split 50-50 and both parents are awarded automatic joint custody of the kids unless one partner is a significant threat to the kids.
In short, I just don't see how a marriage should be a contract between both partners and the state.