Imagine if everyone made a little more money, except for rich people who made considerably more money. Prices would go up and pretty much everyone would struggle to consume as much (or, consume things of as high quality, or perhaps as eco-friendly), but rich people wouldn't really see much of a change in their spending power, since there's few of them and they're making considerably more. I'd argue that idea counters your argument.
Unfortunately, that idea is more than just an idea: https://www.epi.org/blog/inflation-minimum-wages-and-profits...