It is financially unfeasible for most middle class households to pass down their homes to their children due to the estate tax kicking on assets over 100,000 eur.

Inheritance tax for children caps at 20%. That's hardly "unfeasible".

  Social mobility is significantly constrained

Social mobility is worse in the US that in the EU, e.g. see https://www.strategie.gouv.fr/english-articles/social-mobili...