The risk is that a hotter-than-expected June inflation report — one that Fed Chair Jerome Powell recently called among the most important for assessing the impact of tariffs — could slow the pace at which the central bank lowers interest rates. Importantly, that could also throw a wrench into the stock market’s record-setting rally.

Wall Street's main indexes opened higher on Wednesday as investors sifted through new inflation data and digested a fresh round of heavyweight earnings reports.

Removing Fed Chair Jerome Powell might help Wall Street get the lower interest rates investors love but would also risk a weakened Fed unable to make the unpopular moves needed to keep inflation under...