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I don't think it would be a bad thing if the UK started to chip away at the obsession with property ownership by making renting more attractive.
In fact this could be the way to improve the environment, as a higher % of rentals with bigger burdens on landlords would be a more effective way to incentivise greener heating and building investment (insulation) that would be administratively easy to handle (fewer number of landlords involved) and reach more people (more residents per landlord). It would also encourage the development of rental only apartment blocks leading to better services accessible to all renters, i.e. Swedish style blocks with shared facilities.
The countries who forbid mortgages on 2nd homes tend to back it up with laws that give tenants more rights and rent control. As you suggest, the downside is that a small number of people hoard most of the property but the upside is that its not treated as a get rich quick scheme by landlords and tenants receive stability, security and lower rents in return.
I don't think it would be a bad thing if the UK started to chip away at the obsession with property ownership by making renting more attractive.