My home isn't "doing nothing." It is providing housing, independence and security both now and, hopefully, in retirement. If I ever need residential care, it is there to help fund that, reducing my reliance on other taxpayers. I know from experience that many people who fund their own care also pay higher fees than local authorities, effectively helping to cross-subsidise care for those without savings or assets to sell. I traded my labour for a PAYE salary and used that salary, over several decades, to pay down the debt I took on to buy my home. My money has been working hard, and so have I.
Given the costs associated with our ageing population and growing housing insecurity, both of which place considerable pressure on the state, I'd argue that's exactly what a home should be doing. If I don't own my home, someone else does, whether that's the state, a housing association or a private landlord. We do have a productivity issue in this country but the bricks don't suddenly become more productive simply because someone else owns the deeds. They just become an income generating asset for someone else and, increasingly, an income stream flowing overseas or into complex ownership and tax structures the government can't get at.
The real reason housing has become unaffordable is supply issues, planning and policy failures + rising demand. If you want lower house prices, build more homes and limit investment acquisitions / empty homes. I'm sorry but saying that that the sole home owned by someone is idle capital just feels a bit like newspeak.
If the state taxes away peoples ability to hold to onto homes that were intended to provide them with stability, security and help fund future care it increases the likelihood that those costs will ultimately land right back at taxpayers feet. That isn't creating wealth and stability it's bringing tomorrow's money forward to pay for today's spending.