As for if it is a problem of cooling measure of economic failure, I would say it’s probably neither, but it’s the social phenomenon in modern societies – we technically see it in most asset classes like stocks and bonds too.

HDB Problem:
The older generation (those with HDBs) or any sellers would love the prices to be high so that they can sell it for a profit and have a comfortable retirement egg nest.
The younger generation (those buying BTOs and resale) or any buyers would love the prices to be low so that they don’t have to pay as much for a home (lower debt burden).
It’s a struggle (or tug-a-war) between people of different generations and it is tough to say which side should get more help.

Help the Buyers of Houses?:
Sell BTO at the cost of construction to buyers
Buyers can buy cheaper BTO flats.
After the 5 years minimum occupancy period (MOP),