Inheritance is in most cases the only way young people in a lot of European countries can even own their own home
Why are houses so expensive? Alongside challenges and inefficiences related to permits and building (as plenty discussed elsewhere) housing is also used as an investment asset by people with money to invest. This ranges from individuals buying an apartment to rent out, to large investment and private equity firms buying up whole swathes of real estate. When the global money supply is increased (e.g. post-2008 crash, post-Covid, etc.) a lot of it ends up with the rich, who then invest directly or indirectly in asset classes including housing. (Also see how e.g. classic car prices have increased since ~'08).
Until this mechanism is recognised as the cause of asset appreciation and measures are put in place to reverse this trend, the current cost-of-living issues will continue to worsen. Sadly, most politicians are already rich enough to benefit from this situation, and so --in the unlikely event that they even recognise this as a cause-- are unlikely to strongly advocate for measures to address it. Additionally, politics in many countries is too intertwined with big business to mean that such a revolutionary concept would be entertained.
tl;dr: addressing the huge progressive accumulation of wealth by the rich --of which inheritance is one aspect-- is what is needed to address the continual appreciation in so many asset classes, including housing.