The nature of HDB may need to change

[redcorolla95]

Also, another point I have not mentioned. With this method, Singapore can give every single citizen the subsidy (amount dependent only on your income level). Then they just go and choose their choice of housing.

Then it becomes the government transferring wealth indirectly to private developers.

The land cost is the major component of a property price. Guess who owns most of the land.

What would then happen in your scenario would be that
1. property prices would rise to something like Hong Kong
2. but after the subsidy, the net price people pay would be close to what they're paying now
3. and so the subsidy goes to the private developers, not the citizens, which worsens rather than helps the problem