Counter to that, if the PPI is higher than the CPI then...

Counter to that, if the PPI is higher than the CPI then there's already margin compression for the producers as their higher input cost haven't been passed on therefore any sales price drops will disincentivize new supply in a time of shortages.
US simply can't handle less supply of critical products. There's certain products humans can't live without and those are where prices will continue to rise and that's non negotiable for consumers, fuel, food, rent. Higher interest translates to higher rents as landlords will pass on cost. Less sales at higher prices.

A more hawkish Powell means less production as no one wants to run at a loss, China, Russia, Ukraine imports are obviously down also.

All roads lead to Stagflation from my perspective.
Powell will break at some point, he'll have no choice.