As far as we know, most millionaires pay exactly as much tax as they are legally required to.

Indeed. Although it should be noted that due to their phenomenal wealth these billionaires and upper level millionaires are able to heavily influence tax policy through a range of means including, but not limited to, funding “grassroots”/astroturf campaigns, donating to politicians, influence peddling throug super PACs and laundering their preferred taxation systems through think tanks that they set up and connect to the political apparatus.

Various laws that are enormously advantageous to very wealthy people didn’t breathe themselves into existence.