Raising interests rates to slow down the economy is the only solution to inflation neoliberalism has to offer. It's the old Milton Friedman (?) trick, too many dollars chasing too few goods, and those too many dollars must be coming from working people earning too much money. The fact that inflation is primarily caused by profit seeking isn't ever admitted to.
It does cause a different form of chaos (just look at the Volcker Shock of the 1980s for an extreme example), but it's one the wealthy can easily ride out. It even helps them consolidate more wealth, as they have the capital to buy any assets that come onto the market during the recession. See how after the 2008 crash private investment firms bought up most of the homes.
There are other ways to combat inflation, some of those being price controls, market planning, and infrastructure investment, but all those things require chipping away at the power and wealth of the wealthy, so they aren't even considered.