If all red tape were removed, it would take years and years to bring down prices if you are just relying on private developers. It would happen eventually, but would take a very long time.
One possible solution here is for the government themselves to get involved and build homes, this will bring down prices much more quickly. Not as welfare or "low income" housing, but as an actual market intervention. This happened in Australia in the mid 20th century and had good results.