Inheritance is in most cases the only way young people in a lot of European countries can even own their own home
Lack of housing is a disconnected problem from inheritance taxes.
This assumes that each family only gets a single house. With enough wealth you can buy out all the houses (not considering other factors)
If that is not the case, I unfortunately still didn't get your point.
And what do you suggest for those that don't have any inheritance?
Only if you don't build enough new homes in places where people desire to live, because you can own a home - just not where you want to actually live.
The reason there is an issue with housing is the same reason why these articles appear declaiming the political risks (notice, Stigliz only says the risk is political...his friends losing office) of inequality.
This will continue forever, it is ingrained in human nature, it is why it took tens of thousands of years for economic growth to happen from the birth of modern human society.
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.
What do you mean "until"? It's the core of many of European "dreams".
Take UK for example, where there's a concept called "property ladder". This property ladder is the promise of ever increasing property values, to build wealth(it's a pyramid scheme). This "always appreciating" promise is not just subtextual, it's literally the core of the method for becoming wealthy.
Whole economies in Europe are built around this constant real estate appreciation and first-home-buyers' support.
This is becoming the case in US as well, to lesser extent. US has a much more dynamic property market, than the wealthy Europe.
Politicians will bend over backwards to protect this "dream"... and at this point it is screwing over the new generation.
Sorry if I was unclear; I'm not referring to the "housing ladder" here, but rather that the accumulation of wealth (accelerated in recent years) by the already-rich has driven investment patterns that have in turn driven the appreciation of many asset classes that sit behind the current "cost of living crisis".
If one accepts this premise, then an obvious solution would be wealth taxation, of which inheritance tax is one form. But very few people in the politican/economics sphere are seriously talking about wealth taxation. (There are some, e.g. Gary Stevenson, and Zack Polanski is gently flirting with it as a policy.)