Will The Market Still Care About CPI?

Ask anyone who's been following the rate market for many years what the most important economic report is and you're far more likely to hear "the jobs report" than any other answer.  But at many times over the past 2-3 years, the Consumer Price Index (CPI) was arguably top dog.  This only began changing a few months ago, but it has certainly changed.  The question is whether there is still any major anxiety left for CPI.  If it weren't for the fact that this is one of the only big ticket reports that comes out in the blackout period leading up to a Fed rate cut where the size of said cut is a matter of debate, we would confidently say CPI is almost completely inconsequential.  But because of all that "stuff," we can't rule out a volatile response to a big beat/miss.