This is exactly the other side of inequality: if there is a big gap, someone must be taking advantage of this gap. The problem is that most people are losers in this competition.
https://en.m.wikipedia.org/wiki/Global_Social_Mobility_Index
Rent control sounds like a good idea in theory but in practice it seems the opposite, creating two tiers of renters.
The reason why it works is because the government is forced to change laws that prevent the construction it just promised. It's about accountability rather than the promise itself.
The reason why rent control doesn't work is because the government can enact or keep laws that restrict the supply of housing. There is no accountability. It's actually equivalent to censorship. If you want the housing market to look good, just ban bad news (high prices).
So you have very high wealth inequality, average German net financial wealth is equal to Greece and Germany has a significant number of billionaires, but you also have a system that fundamentally cannot be compared with the US. It just optimises for different things.
That being said, whilst recognising those differences, lower wealth inequality is not the result of most of these systems. Income inequality is generally lower but the cost of this is usually: low competition, high structural unemployment, weak unions, low levels of business creation...it isn't free. It is readly apparent from the EU that whilst the US has high inequality, it also has a far more dynamic economy that results in more people actually becoming wealthy (to take Germany as an example, most billionaires come from families that got rich in the 30s and inherited...the level of downward mobility is very high in the US) and higher levels of innovation.