In my opinion, the problem is not inadequate land.  There is more than adequate land resource in the hands of the property developers.
The true problem is the high property price, which is hardly affordable by most people.
If the Government has the guts to confront the property developers to protect the well-being of the people, there is no need to build public housing.  After all, public housing is anti-capitalism.
An interesting fact is:  "Hong Kong is the least affordable housing market for eighth time in a row", whereas "the ten most affordable housing markets are all in the United States"!  ( ... -eighth-time-in-row)