Community builds housing. Society makes it.
First off, yes a house is capital - within the current capialist system it's capital cost is completely disconnected from the actual capital cost.
Secondly, I'm open to alternatives? I've got an option but a problem doesn't have to have a solution for me to point it out. That doesn't mean I don't understand capital.
Here's an "alternative" people get their personal property. Secondly we give out empty homes. You can trade homes, hell even sell em but their value isn't the same anymore after revolution and everyone owning one.
All the way down we have established communes. Communities that we partake in. Here we would build housing when new families need it. Community effort to make it in a fairly moneyless society.