Maybe it's different in the UK but I haven't heard the term "housewife" used since never unless it was referencing the 1950s.
In the states there are almost always options under 'occupation' that state 'stay-at-home-mom' and even 'students'.

Neither of which is technically an "occupation" which is defined as a means of earning a living, but I would consider them work. Just because it's an "occupation" doesn't mean it's hard work and just because it's not an occupation doesn't mean it's not hard work so I don't see what's wrong with having a distinction between having an occupation and being a stay-at-home mom since neither defines a person's work ethic or the level of difficulty.

I understand and appreciate the point, but in real life if someone were to tell me that their occupation was "mom" I would think that's reaching and would not agree with 'stay-at-home-mom' as an occupation.