Here’s what I would propose.
I would happily accept rental caps on private rentals IF, the tax on rental income was reduced or abolished in addition to the eviction of rogue tenants being more expeditious. That way, the tenant wins with low rent, the landlord wins with security of assets / income and the state wins with less homeless due to less landlord leaving the market.
Make high quality, high density housing in the cities, for example in Dublin between the canals there should be a minimum height of 100 metres.
Abolish (or defund) whatever you want to call it An Bord Pleanala and the Georgian Society. Reject all objections to builds unless they have a potential serious impact.
Build high quality and frequent high speed public transport out to satellite towns.