If I were to cohabit with a man I do not want him to gain any rights over my home, either on splitting or if I die. That home is for my children. I would purposely not marry to prevent him getting rights
This is the absolute classic case of when marrying is not a good idea - when one or both people already have children, won't be having any together and want to make sure everything they have passes straight to their kids.
And as you say, it's also why marriage does need to stay as an opt in. It's a legal contract, you can't force that on someone or introduce it by stealth. You want people to be able to cohabit without marrying if that's what they want.
Want a legal commitment, with the accompanying protections? Choose it, opt in. Don't want it? Fine, just stay as you are.
It drives me crazy when people insist that they should be married without being married.