Except this inflation is not a direct fee charged to every holder of money. Inflation primarily affects people purchasing consumer goods.

If anything, inflation is the hoarding.

Rich people indirectly hold money by owning shares in companies that hold the money on their behalf. If the money is paid out via stock buy backs, the money is in the hand of the investor. Said money is reinvested into companies, those companies may temporarily pay out salaries, but eventually the money returns back to the investor leading to a dynamic form of hoarding. They started with less money but ended up with more money. The only way dishoarding can happen is if the money is spent on consumption.

Let me repeat:

If you understand the above, then inflation doesn't impact the rich who don't consume anything. If anything the opposite is true. The government/central bank throws just enough money into the system to prevent the economy from collapsing from the hoarding since money is needed as a tool or utility the same way housing is needed. As far as we know the preferred method of giving out that money to cause inflation has never been helicopter money, it's been quantitative easing which historically benefits the capital markets more or basically made the government take on more public debt.

Then there is the fact that any system where income is proportional to ownership basically negates the impact of inflation for said income. If you earn 3% yield at 3% inflation you might say that this nets out to 0%, but it doesn't. In nominal terms that is still a net inflow of money. You might counter that multi billionaires only turn into trillionaires on paper from inflation but they are still just multi billionaires. The point is that despite this real yield of 0%, the total share of money held by said multi billionaires can still go up and increase inequality even if in real terms their actual wealth did not change simply because consumers pay inflation and the billionaires don't.

If you ever bothered doing even a little bit of research the standard solution to "growing past money" is either something like a demurrage currency or the banking version called oeconomia augustana by dieter suhr (the bank charges a liquidity fee on both positive and negative balances to encourage getting to 0 residual balances, the liquidity fee is automatically determined by competition between banks, it is essentially a private implementation of Keynes' bancor proposal).