Affordable is about supply and demand. Build enough and all houses are affordable. Don't build enough and people will find ways to cheat to get what you make as 'affordable' so they get in.

Of course there will always be people taking advantage of every system. I think it's more problematic when the people setting up a system is also participating in it. See: US Congress making rules for itself, including stock trading (small potatoes) and corporations investing in politicians for massive returns (very large potatoes)

Not-so-poor people playing a game well that results in massive benefits? A mere distraction.

>Build enough and all houses are affordable.

There are more vacant units in the US than homeless people. There is some nuance in how the market functions - it happens to be profitable for large private landlords to set prices higher. The market does not exist to optimize the number of people who have housing, it exists to optimize the amount of money that landlords can make.