At cost home ownership for low income / lower-middle class residnets

Many of us are tired of throwing away money on rent every month. I'd love to be putting cash toward a home, but that's nearly impossible and impractical in a lot of major cities-- especially if you're single.

This would be ideal for (but not necessarily exclusive to) first time home buyers. A building with X number of units sold at cost. 0% or very low APR. Even a $100,000 unit at 3% APR for 30 years still comes out to just $422 per month. That's much better than renting a small apartment for $700-$1500 which is very common these days.

Some details would have to be worked out to prevent people from immediately flipping them for profit, but I'd really like to see something like this happen. If it's already happening, I'd like to see it become commonplace.

Not sure if the best option would be government involvement, philanthropists, and/or non-profit organizations, but that's the basic idea.

Any thoughts? Seems like this would be a great way to help strengthen the middle class.