Why do you want to give local authorities a stake in growth? Haven’t they proven to be a failure?
One of the causes of the housing crisis is the way local authorities are funded. Central government has repeatedly put demands on local authorities without funding them accordingly. A good example is the Government allowing rapid population growth but not allocating local authorities funds to invest in infrastructure, e.g. water, public transport, cycleways, local roads, parks.
Most local authority revenue comes from rates, so they have had to borrow to build infrastructure. Now some local authorities have hit their debt ceilings and can’t afford to invest any more. Meanwhile, ratepayers (who overwhelmingly tend to vote for local authorities) don’t want higher rates, so they vote in councils that limit investment in infrastructure and curtail housing supply.