The mechanism of higher rates reducing inflation isn't clear to me.
Does it go down because people with cash choose to park it and earn interest instead of buying goods and services? Or does it go down because higher interest rates make the cost of doing business more expensive which leads to reduction in overall business activity?
If it's by reducing business activity, then seems like the "breaking point" can be at any arbitrary interest rate for a given country in a given year.
Also, if inflation is caused by the lack of supply (like the supply chain issues / chip shortage and such), then I think reducing business activity will only exacerbate the problem by reducing the supply further (and I don't hear anyone explore this angle).