People want to be in close proximity both to their jobs and to the businesses they want to patronize. Your suggestion would reduce or push away those businesses but retain the dense housing stock, but whose value would dramatically drop because those businesses are restricted or moved. You've created slums.
It is not necessary to obliterate the local business environment, only to limit it to the extent that the available jobs roughly match the available workers. Yes, it is true that house prices would fall to be more in line with construction costs, but that is the point, if you want cheaper housing, the housing must actually be cheap.
This talks about it a little without fully committing to the actual problem https://blog.lgim.com/categories/investment-strategy/why-lon...
Seems to me remote working and the improvement of "cheaper" areas, organically (as more people spend money in these areas and increase demand for services there) is the most viable solution but something governments can't seem to grasp or choose not to grasp
I hadn't thought about remote work and you're right. It's an excellent solution, at least for the jobs that don't require presence. I don't think politicians necessarily need to do much for remote work to be successful, as long as they don't block it. It is very attractive to employees, because commuting is terrible, and I have seen a lot of pressure in companies to allow remote working. Hopefully it will be more widely adopted in the future.