Might be

ESE affects how fast the divisions stockpile fills up. If you are advancing really fast you outrun the supply and the stockpile goes down.
Even if you have a full stockpile of supplies the infra and ESE of the province your division is in will affect combat.
Its IMO the major reason you have to slow down. Divisions can get some nasty supply penalties if you advance to fast.
Not a big deal as long as you don't face any resistance, but if you do you might end up having to turn tail and retreat.
This issue is very pronounced in Barbarossa. You have to advance very far in to Russia to trigger the peace, which is stretching your supply lines pretty thin.
Getting a bit off topic though, but what I find strange is the reduction of infra when capturing a province without combat.
Why would the roads get destroyed when the army is not doing any damage to it?
IMO the reduction should be reduced if there was no combat.