Lowering property prices by raising interest rates, makes it more difficult to afford houses and implies killing the economy and putting people out of work. Home prices usually end up going down only because people are made not to be able to afford them. This is incredibly destructive and it only allows more people to live in the same area when they are forced to move in with their parents.
I used to think rising house prices were a bad situation for us millennials but now I believe this to be a best case scenario.
It is impossible to keep adding people to the same space while giving everybody much room for their money. The problem is trying to cram a generation of millennials into the same area as a wealthy cohort of boomers and rich immigrants predictably makes home prices go up.
Increasing supply or nudging the new generation to go in areas with more potential for spacial growth not only allows the new community to be built to the image of its own people but building and growing the infrastructure of a new neighborhood or revitalizing a dying town creates jobs for the people that go there.
The best thing governments could do to help with this situation would be to encourage some of the institutions and jobs relevant to new generations to move out of overpriced, overcrowded centers. They could foster jobs creation in centers with more low cost space and less chance of spacial overload. They could maybe move some public jobs there to help jump start the migration. This would also put some downward pressure on the prices in overcrowded places until we reach some kind of equilibrium.
I say stop trying to cram everyone in the same volume. Let the older rich generation keep the expensive quarters they've spent their life building and allow new generations to create our own communities, in our own space, from choices guided guided our own tastes.