I think you are confusing two things. The poor may struggle to reach ends-meet more than the rich, of course. But that doesn't mean that relatively speaking inflation is a regressive tax that the poor have to carry the burden of disproportionately.

> No, wealthy people tend to invest theirs saving in various things that resist or often even beat inflation.

This is easier said than done. Given a risk-free rate it's not that hard to find investments that beat it. What usually happens is that the risk-free rate is around inflation. But right now the risk-free rate is significantly lower than inflation. If the Fed raises the risk-free rate to match inflation then high valuations will correct resulting in a strong correction in the stock market.

SP500 historical chart: https://www.macrotrends.net/assets/images/large/sp-500-histo...

Look at the 70s, same period of high-inflation I was referring to above. The wealthy didn't beat inflation back then, which again is reflected in the previous wealth inequality chart.