Self employed domestic stuff is a very small fraction of it. I have no figures but this is based on what i see regionally.
In the south, it is mostly all farm labor, civil construction and forestry. In other areas it is much the same with some areas having more restaurants, gardening and landscape work.
Much of the janitorial stuff in contractors and I suppose I should not forget the migrant tomato pickers , fruit pickers and others.
I would say, the majority is in agriculture.
Miss them?
In Arkansas, it would be devastating to our only industry, which is trees, chickens and rice, cotton and soy.
I doubt it would be devastating. America had a strong economy long before the massive immigration of the 1990s. The region I'm in has extremely high immigration and the highest poverty rates of the USA --- also very high unemployment and welfare rates. Even states like Michigan have high unemploymnet rates --- something over 7% --- you'd find workers if you paid more than $3-4 an hour and maybe offered a little health insurance for those jobs.