If one partner earns more and pays a disproportionate amount of the downpayment and mortgage on a house that both partners live in, is the house really only 1/2

If one partner earns more and pays a disproportionate amount of the downpayment and mortgage on a house that both partners live in, is the house really only 1/2 theirs legally? Ethically? Makes sense to me. If say, the dad stays home to take care of the house and look after the children, while the wife works. Should the husband then be left with no claim to money/house if the wife decides she wants a divorce? Maintaining a house and raising children are not low effort jobs. If you calculate how much daycare + a basic cleaning service would be year round, I doubt the cost would be minimal. Not to mention the fact that the person staying home will undoubtedly have a tough time entering the workforce after an extending period of time away from their careers. Even if both work, how would you go about figuring out the split if the incomes were inequal? Do you literally just take the incomes and proportionally divide up the assets accordingly? What if the person earning more doesn't actually contribute their share to the mortgage, and wastes money on frivolous expenditures? How do you actually decide what is fair?