The EWC applies to all property. Not just land. If they take the patch of dirt your house was sitting on, they will take your house as well.
You raise a good point about what ownership actually means. However, they key difference between owning and leasing is that if you own your house, you are incentivised to improve it as your family can inherit it or you can sell it.
If the state owns your house, you can be kicked out for any reason they want, and you won't do anything to look after it as if you do anything and the state notices, they will kick you out and put one of their friends in it.
Here is a hint, don't look at the ANC like a government. Look at it like a patronage network. People only move up in the power hierarchy when people in the branches vote for them. How do you get people to vote for you? You promise them an easy job with lots of money. How do you get easy jobs that are well paid? You control the government.
NHI is nothing but a patronage network for the health minister as it will place the countries entire health system under the lminister. Just think of how many admin jobs you can hand out.
Ditto with EWC, all you need to do is promise the influencial people in your branch a nice house and you can get the state to take whatever house they want.