There's a fundamental disconnect in how the economists in this paper view profit and how companies view profit. Essentially, their theory is that if we raise interest rates, this will subdue demand, and thus tame inflation as companies drop prices to compete for a smaller market share.
The problem is that the companies that control the core essentials - food, energy, and to a growing extent housing - are effectively monopolies. Markets that had hundreds of competitors in the past now only have a few dozen at best, and they actively use their vast power and influence to reduce the capacity of any smaller players to participate, let alone compete in the market.
You can't reduce demand on core essentials, because people can't do without. As a result, in a monopolistic market, an interest increase only harms the consumer when it comes to core essentials unless a company decides to reduce prices and subsequently their profit.
There is no publicly traded company on earth that will voluntarily decide to lower their profit. The only way they'll do it is if it's hurting their bottom line - aka through competition. With no competition to reduce market share, effectively the company can simply keep pace with interest rates by continuing to profiteer, especially when they're operating in markets without price controls. In those that do, the companies often engage in aggressive regulatory capture to ensure a steady profit margin well above cost, regardless of the market conditions.
In our current situation, interest rate increases will do little to nothing in the short term save to tighten lending and push home ownership out of reach of the middle class. We will not see drops in prices, only a leveling off from increases, as consumers have come to accept them as the new normal. Rate increases do nothing to address the core issue, which is that the extreme consolidation of wealth in a handful of companies has given them a power over our economy far greater than the central banks that claim to run it. If anything, those rate increases encourage the same consolidation of wealth and monopolistic markets that have led to our current economic state.