We've been under-building for decades. Let's give not doing that a shot and then we can talk about other approaches if that fails.
- Remove (or greatly reduce) zoning restrictions to permit things like ADUs or re-development of single-family plats
- Enforce rent-control via legal means (which is what your guaranteed market-rate solution sounds like - although I don't understand how this solution would work with your stipulation that it be "impossible for the [government] to demand affordable housing subsidies")
Or is there something different/more that you're envisioning?
My view is that it’s pretty silly to talk about other solutions so long as it’s literally illegal to build housing. We should just try making it legal for a couple decades and then see where we are. This is not a problem that demands creative approaches.