There are a ton of issues with our economic system, and there are a ton of structures in place to funnel money up, but keeping a moderate inflation is not one of those things.
Inflation is a specific counter-measure against people who already have a ton of money. It provides a reason for them not to just “take their ball and go home” once they have a pile of money.
To shelter their money from inflation, they need to either risk it on the open market, allowing that capital to do things like pay worker salaries, or buy things like GICs which are essentially loaning money to the government so the government can do things like build roads or fund social programs.
In either/all cases, inflation is designed to do the exact opposite of funnel money upwards, it’s a mechanic to wrench that money out of the hands of the wealthy.