Marriage and cohabitation are not the only two options, I’m afraid. You could have plural marriage. You could break up entirely. I’m sure if you thought about it, you could come up with many different models for relationships. You could marry but live in separate places. You could not marry, but be exclusive with each other and live in separate places.
You need to look at what both parties want out of the relationship. You mentioned respect, communication, financial cooperation, children, religious participation, community participation and more. I would add companionship, alone time, business partnership, travel partner, caretaker, intellectual companion, and probably many more. My guess is that you could build a scale of all these things, and the more people want overall of all of them, the more likely they will be to marry.
However, some people may want a close relationship, and yet not want to live together. They may not want children. They may not want to share finances. Still, some may see marriage as an expression of commitment, even if they don’t want to spend time together, so they may still choose to get married even though they don’t want anything else.
Similarly, some people may see it as a financial relationship more than an emotional relationship. They may want to marry in order to get the financial benefits of marriage, but may have no interest in really sharing a bed or even food. I think this is illegal if you marry someone to make them a citizen, but it is ok if you are both Americans. Citizenship can be a marriage issue.
This is all to say that I think you can make compromises on the form of the relationship. There are many forms of marriage and cohabitation. Those labels cover quite a lot of behavior.