Are the Fed’s higher short-term rates the right measure to fight inflation?

Are higher short-term rates, the Fed’s primary tool, really the right measure to address the causes of the inflation we’ve been seeing for over a year?

We’ve been hearing a lot about the 70% increase in the price of eggs. But that was caused by the bird flu. Can a higher federal funds rate really fight that cause?
What about the steep increase in energy prices worldwide? This is largely down to the Russian invasion of Ukraine. Does Putin care about the Fed’s action?
Or the supply chain issues? Do higher interest rates solve these problems? The Fed’s rate hikes can only impact demand and will do nothing to ease supply bottlenecks.
And the shortage of workers has driven prices up in many industries, particularly services. Lowering economic growth through higher rates will also not bring workers back into the labour force.

All these causes are largely disconnected from interest rates.

Sven Franssen