When the purchasing power of currency goes down, the people with the most currency actually lose the most, meaning the rich. In this way, there is a flattening effect. In cases of hyperinflation, having 3 million dollars is scarcely better than having 300, and money is revealed to be the apparition that it actually has been all along. The negative impacts of being unable to purchase basic goods and services also acutely affect the working class, but in a lot of cases that's already true in a "healthy" economy.
This is the reason the bourgeoisie is always pulling their hair out about it. It's also only ever used as a pretense to do austerity and extract even more wealth from the working class while cutting basic services.
Since value comes from labor instead of markets or scarcity, inflation also literally wouldn't effect our standard of living in a meaningful way at all if we set in place robust mutual aid networks and centers and divide the labor in a more just way.
When the narratives of capitalist realism and market necessity start to erode, this is actually a good thing, and this is the case with inflation as long as we are organized and prepared to exist beyond the market.
It's not really that inflation is an equalizing force, but rather that it forces a reckoning with the socioeconomic power dynamics inherent to the money system.
Additionally, no regulatory power or dude in a suit has the ability to force price controls without the tacit permission of labor.
What inflation does best is make the lack of credibility due the charlatan neoliberal prognosticators plain to see. It creates a crisis of confidence in the system at a level the majority of people cannot choose to ignore.
Finally, and I hinted at this earlier, if we take the labor theory of value seriously as we should, prices do not effect real value literally at all. The barrier to having basic needs met isn't the fabricated, ad-hoc scrawlings of self-styled technocrats, but rather the lack of community, will, and organization requisite to stop asking our bosses and landlords permission to take care of each other by any means necessary.