What government can do is make a concerted effort to lower housing costs so that jobs become tenable. It's no good pricing many jobs out of the market by huge living costs then expecting temporary workers from overseas to do them. That way lies madness. Benefits to support wages too low to allow people to afford a roof over their head helps no-one in the long term. Mass building of real council houses will help the situation. Use the QE interest money to get the ball rolling, rule out housing associations and make sure they're never sold.
I absolutely think we need to build more houses and that housing costs need to come down. but it doesn't really help with economic growth...
...and that has to be a priority at the moment. if you're going to borrow for capex you need to do it in a way that will generate or facilitate the generation of income. transport infrastructure is a great example of this. but there are more modern examples around IT. building schools. stuff that will pay you back.
as for the specific allocation of one source of revenue to one source of expenditure, it's economic nonsense. it's a thing that only exists in the minds of politicians. it's not real.