Inflation benefits the people that have more wealth because it props up their assets, while it goes against the people that earn a wage (usually the middle class and the poor) because it devaluates their wages.
Isn't this the reason we have cost-of-living wage increases, bonuses, etc? Inflation also benefits mortgagees (and other debtors) by reducing their debt in relation to available currency.
The basic mistake you are making is believing the wealthy keep their wealth in currency. They dont.
Neither do the working classes. They spend it. It's a currency --
If one's exposure to the dollar is limited (i.e., hedged via DXY [or similar] puts), how does inflation hurt him?
If the working classes want to save or invest they buy stocks, bonds, mutual funds, or what have you (ideally based on advice from honest financial advisors or they merely leave it to the fund managers [essentially with hedging and diversification built-in to the funds themselves]).