Let’s be real.What can stop Fed to be hawkish?

I still see some ppl commenting like,”Fed won't be hawkish as they say”.But obviously market always prices in what Fed says and market is right.Powell repeatedly said that inflation is their priority,they don't care with your market gains nor stocks with 90 pe.He also said that Fed will use it's tools to fight with inflation.Tools are obvious, interest hikes and balance sheet tightening.
On the other hand recession is coming ,but Fed even can let recession happen to eradicate inflation.So what can stop Fed to be hawkish?First answer is easy: inflation falls and Fed puts the dowish mask.In case inflation maintains but unemployment rises significantly then Fed has nothing else to do but dropping interests to zero once again.That's why unemployment data will be key as soon as we enter to recession which is likely coming in July.