False, this mechanism only prevents income inequality but not wealth inequality as existing wealth is not taxed much in Europe.
For example, inheritances, assets and properties are not taxed much in Europe (people scream double taxation if you propose that) but income is taxed substantially so you'll never be able to save enough to catch up to the upper classes who own assets.
So actually, in some European countries, while having low income inequality because of high income taxes, you end up with huge wealth inequality due to untaxed inheritances, assets and overvalued properties rolled over across multiple generations to the point where Germany's top 10% own two thirds of the country's wealth:
https://www.iamexpat.de/expat-info/german-expat-news/germany...
To level the playing field and reduce wealth inequality, a sound policy would be to tax income less and tax inheritances and assets more but fat chance of that ever happening as that would be a blow to the ruling class.