I don't think people moving from SH to private rent will be particularly productive long term.
Private rent is unstable, expensive and isn't regulated enough when it comes to repairs and maintenance - meaning you're moving people from fairly priced and stable accommodation that should be (that's another story) fit for purpose, to more expensive, poorly maintained and lack of security. There's restrictions on things like putting up pictures and having children or pets - fine I think for short term lets that people need, but unnecessarily restrictive for long term lets that will be needed to meet the needs of those moving from SH.
That's going to create problems as private rents rise more and more, people are evicted for whatever reason they can be when a landlord wants more money or to sell, and can't find or afford anything else and end up back on the SH register - all of which could have been avoided if they'd stayed in the SH in the first place.
Private renting needs to be stable and done professionally without these 'accidental' hobhy landlords that need to sell when they realise it's not all about just filling your bank account and that you do need to be proactive and deliver more than bricks and mortar. Run as proper businesses that recognise they're delivering a service, in return for what is not an insignificant amount of money.
If you sort out the private sector and it works for everyone, not just the landlords then more people will be not just willing, but able to use it, freeing up spaces for those that aren't able.
I would be, but I'm not giving up a secure tenancy where I'm dealt with somewhat professionally (there are exceptions to that, it's not all moonlight and roses) have fair rent, can put a picture on the wall and have a dog or cat, and generally live without fear that something will change in my LLs life that will then upend mine. Spent 10 years of that, with a child in tow, and I'm not volunteering for it again!