I think the problem here is twofold.
Firstly, who makes decisions about the home and children? SAHP often think that as they are at home that is their fiefdom. Fine, if both partners have equal standards and ideas, less so if they don’t. Remember, if you were both working and sharing/subcontracting the housework and childcare, you would have equal say in this.
Secondly, divorce can always happen. Then, generally, the SAHP feels the right to half the assets but is very unwilling to give up half the parenting (and often, the nice comfortable family home) and can make the case that it is in the children’s interest that the WOHP keeps paying but loses time with their children, very unfair.
If both parties are happy and the relationship lasts and especially if one is a high earner, a SAHP can work brilliantly but, in this day and age, it is a high risk strategy.
I think that if you are to remain a stay at home parent you both need to outline exactly what you expect of one another.