Part of the problem is government regulation. In some places, it's almost impossible to build new houses due to regulations. Some portion of the population wants to see house prices continue to increase and they will vote for politicians who will implement policies which will support that agenda. Of course this happens at the expense of another, also large portion of the population who do not own a house and have to…
Among my friends seeking to buy houses, the greater problem is the ability of large companies to buy up whatever is on the market, which they then immediately turn into a rental. It’s nearly impossible to compete with a company who will pay $50k over asking price, in cash, for the house you’re trying to get. Comparatively, immigrants don’t have the purchasing power to compete, so saying they’re the problem is a weird…
Does that even matter? They don't have to compete on house purchases, they just have to increase demand on rentals, even at the low end. This pushes everyone in an income bracket above them to compete for the higher priced rentals, until those say "screw this, I'll just buy" find out that even that's no longer possible.
In this game, it's possible for everyone to lose.