For any PM to use power against a province's populace to get at its premier would be punching down, and would directly fuel populism.

That's how conservative premiers get away with slashing budgets and then begging the feds for help again and again, playing the victim card while playing to conservative sentiment about cutting public spending. A counter should be to point out the shell game, or cut a deal where the feds match provincial funds at some ratio to keep provinces from offloading all costs upstairs. The feds don't have to cut a deal, so that's the leverage.