Every online form I've seen offers housewife/househusband or homemaker. I suppose they could get slightly high-tech if they wanted and specifically offer 'housewife' as an option to anybody whose name is Miss/Mrs/Ms and 'househusband' to a Mr- although that would just complicate things more if your a Dr or Prof etc.
It's purely about statistics and risk-based pricing. I believe that they tend to look negatively at 'unemployed' and quote higher premiums, because maybe unemployed people are statistically more likely on their books to make more claims - whether having more free time to drive around or (they may believe) are less careful than people in a stable job. They might also factor in you being possibly more likely to default on your monthly payments if you have a low income. Not saying they should, just that they might.
By declaring yourself to be housewife/househusband/homemaker, you're declaring that you're not in paid employment and aren't wanting to be - presumably because you are in an apparently stable relationship and have a husband/wife in a responsible job who earns for the family and the chances are that you have children and will be at home (or local) a lot with them. Essentially, they see it as much 'worthier' than being unemployed.
'Housewife' doesn't mean 'married to the house' - it's just shorthand for 'a wife who is based in the home' rather than an external workplace.
I do the insurance for both our cars, including the one I’m a named driver on. Insurers don’t care!
They don't care whether they have a valid contract?
I realise that, in MN-world, everybody is an isolated individual who shares nothing financial or responsibility-wise whatsoever with anybody, but in the real world, most married couples will tend to have one spouse who looks after insurances and the like for the whole family, with the cost of all insurances very likely coming from the one pool of family money. I deal with all car-related admin stuff for our two cars and technically, we are two distinct individuals who each own one car and happen to be a named driver on another; but in practice, we just have two joint family cars that either of us will use - like a great many couples, I expect.