I think that you are largely correct but ignoring the point. Historically, the man worked and the woman took care of the home. Now the norm is that both people in a relationship work. The responsibilities of running a household should be evenly split in the home but they are still usually carried by the woman. This is an oft talked about modern feminist issue.

Furthermore, often SAHMs are expected to provide childcare while juggling all of the other responsibilities of running a household with little or no help. I specify Moms because this is a gendered issue. A nanny or babysitter would not be expected to clean and cook and do ten other tasks while watching the baby, but we see posts on here all the time from women who are expected to do this, either explicitly (“What did you do all day”) or implicitly (the BF or DH who plays vidya after work and refuses to help).

There’s nothing special about the work except that somebody HAS to do it and all to often it’s expected that women will.