A mixed property market is probably going to be the "best", rather than a one-size-fits-all approach, but as you say it isn't a problem of balance between social and private it's simply that there isn't enough property, in the places where people want it.
The issue I have with the Tory's idea (aside from the remnants of the ideology of my youth) is that we have data that it does not in any significant way increase the number of properties available.
We need to build more properties and to me this one it's a real puzzle why no party actually seems to want to tackle this, there seem to be a number of simple (in comparison to many other social issues) policies they could adopt, at very little cost to the public purse to massively increase the housing stock.