The current inflation is primarily caused by high energy prices, secondary by shortages (semiconductors, grain, vegetable oils, etc) and third (delayed effect) higher wages due to worker shortages.
In theory, a rate hike reduces demand. But it won't for the above goods and services as they're barely optional. People are going to continue to heat their houses, vehicles will keep moving, factories won't be shut down at scale. People won't stop eating either.
I believe the much more aggressive rate hikes by the FED, multiple already, validate this point. It's not done nothing to reduce inflation.
I'm thinking it's going to be energy savings (by consumers and industry) and working on energy alternatives/abundance to really kill high inflation.
Another example of a non-working instrument: here in the Netherlands the long term mortgage rate (15-20 year fixed rate) has more than tripled in just 4 months time. It doesn't even move the needle in house prices. It has slightly slowed down growth, and that's it. The reason it doesn't work is because there's no supply and the demand is not that elastic. People need a place a live.