Think of Offensive as a 'adrenaline-rush' for your units. Its costly, but very effective and can and has turned the tides in battle with me. Getting those African based units under UK control booted out of the continent as Italy is a big ask.
It is my understanding that Offensive is meant to mimic the logistics changes from a unit in the barracks to a unit in a fight.
In barracks, a few rounds issued to those standing guard duty, minimal stockpiles of needful things appropriate for occasional training and basic day to day business of a military unit.
In the fight, the ammo and other needful things, stockpiled at various levels of command to ensure "good enough" flow forward of logistics in order to sustain a unit in battle.
In battle, I have my units on Offensive. Otherwise, it seems to me that I'd be sending forces out into the fight with only whatever they'd be expected to have on hand when in barracks.