It's not subsidised just because it's cheaper. If a private landlord had bought a house back in 1996, when they were much cheaper, she could afford to charge a much lower rent. It wouldn't be subsidised, because no-one is putting in money to reduce the costs. It's just that the landlord can afford not to charge market rent and chooses not to.
Similarly, most council/HA housing has been owned for a really long time. The costs of building the properties have been covered by the rent payments. So the council/housing association can afford to charge cheaper rents, and that is the point of them.
Stock-transfer HAs (where an LA sold their whole stock to an HA) will have a loan to cover the cost of the properties - essentially a huge mortgage. So rents go to cover that, along with repairs etc.
There is some capital funding for building new social housing - this is a subsidy, but it's a miniscule proportion of the whole stock - not enough to affect rents overall.
So it's not subsidised rent.
It is a public asset, and it's not being utilised well. It's wrong that there are families in temporary B&Bs when there are homes being under-utilised. It's wrong for them and the extortionate costs of temporary accommodation are being paid by local authorities.
But I don't think it should be solved at the cost of the benefits of security of tenure for social housing tenants. Because those benefits aren't just for the individuals. We all benefit from stable communities. Being able to live near your support networks reduces loneliness, mental health issues etc. it makes for nicer neighbourhoods. And it says people are valuable.
I think it should be looked at in the same way as bed-blocking in hospitals. What is stopping people downsizing? What would enable them to move?