"For example, I believe in most (all?) countries, if one spouse assumes a financial liability, it automatically extends to the partner (yeah, this is a simplification). This does not hold for unmarried couples. One could have a system in which no such solidaric liability existed (but solidaric liability is a practical thing for couples who share economy and the (financial) responsibility for children), or one could imagine the courts on a case-by-case basis decided if a couple was considered to share a particular liability (but that would create a lot of uncertainty, and legal expenses). "
This is not true in the USA and I would expect this to not be true in many other countries.
If one spouse assumes a financial liability it does NOT automatically extend to the other partner. For example buying a house or a car or stocks or bonds, etc.......
As for children....the financial responsibility is there whether you are married or not! In fact many if not yet most children are born out of wedlock. In fact the children may be born out of a rented womb.
So I still see no huge reason why governments should be involved in whether a marriage is legal or not. If you want some legal contract, see a lawyer! IF people come to some meeting of minds, fair enough they have formed a civil contract, that can fall under civil contract law. I still do not understand why taxpayers need to be involved in weddings or marriages. Let the private sector handle it!
OTOH for those that view marriage as a holy sacrement I can understand religions that may very well have rules for what a legal or illegal marriage is.
OTOH if you want to define what a marriage is so you can give them tax breaks....and discriminate against those who are not married, ok.

I can only see the government getting involved in what a legal marriage is if they want to discriminate!
If businesses are going to discriminate against those who are not married, sue!