Both housing and health are systems created to limit the size of the city while also allowing you to manage it somehow and deal with it (by buildings, civics etc.). The implementation is similar, but different.
I personaly think that housing makes more sense, because it directly relates to number of people in a city. But the implementation in Civ6 is not really perfect and some attributes are not very intuitive - for example why settling near a river provides housing? Yes, we can create some explanations if we really try, but the first thought will probably be that "people don't live on water, do they?" or "rivers were important, but they provide water and food, not houses".
Btw I didn't like health in Civ4 very much. There were too many parameters per city which all were different, but in the end worked similarly and you had to manage all of them by the same actions (buildings, improvements, wonders...). It was too much micromanagement.