What's this obsession with increasing housing density? Population in the developing world is leveling off. Most of the developed world is already at "peak child".[1] Housing shortages come from migration to cities, not more people. [1] https://ourworldindata.org/peak-child
Wealth inequality is compounded when urban real estate appreciates faster.
The Economist blithely ignores why governments are obsessed with homeownership, though--because homeownership tends to negatively correlate with wealth inequality. That is, the greater rate of homeownership, the less wealth inequality. So rents may be stable in Germany, but so is its moderately high wealth inequality.[1]
However, mortgage burden positively correlates with wealth inequality. Using easy financing to make ownership more common tends to cancel out the former effect. So, really, what correlates with lower income equality isn't nominal ownership, but actual equity.
[1] See https://www.oecd.org/officialdocuments/publicdisplaydocument... and https://www.jstor.org/stable/pdf/10.15609/annaeconstat2009.1...