If the government overspends, the central bank has to compensate with tighter policy to achieve the inflation objective. So long as this is commonly understood, an inflation-focused framework means better coordination between the government and the central bank as they go towards the common goal of macro stability.
In this regard, looking at annual price changes across all CPI items less fresh food, the share of price-increasing items minus the share of price-decreasing items has been rising on average recently. In this situation, I believe various changes are spreading throughout the economy.