That the left would do a lot for the common people, I consider hopeless optimism. You only have to look at Berlin where they have been in government long enough. Where are the big housing construction programs that one would need? Making it better for everyone is a bit more complicated than taking something away from "those up there" which in practice almost always hits "those in the middle." The very top always find a way to avoid a burden, but as an employee I already have my money taxed and have to reclaim a few hundred every year.
That it is difficult for middle-income earners with construction costs, I believe there is no discussion. The house itself, I believe, is only part of the problem; it is mainly the land. With the land prices, many have their equity gone and are dependent on the bank's drip from day one. Every fee for architect, surveyor, etc.
And the problem is that you can hardly influence the land costs yourself. Whoever finds the house too expensive can still build with a gas heating system following the Energy Saving Ordinance and wallpaper the walls themselves. But there is not much you can do about the land.