Just speculatin so without prejudice:

A supply wagon does affect battle morale in a negative way: if it is sacked your army gets worried where its next meal will come from. IIRC Alexander's army worried when the wagons went at Gaugemela etc.

A supply wagon means your army can travel faster and further (doesn't disperse to rape and pillage).

In some basic ways supply wagons have a strategic effect similar to generals: if they die in battle the army gets a morale hit and so on.

Maybe there should be a recruitable general with a slow non-combatant wagon bodyguard for civilised factions? With healing, speed and other boosting ancillaries. Then individual units could be represented by limited recruitment or mercenary "Eagle" units.

It would need to be modded heavily to avoid looking ludcrous: imagine a pop-up announcing your faction leader (a 50-year-old 12 oxen dray) has sired a new offspring (a two-wheel cart) or has acquired the trait "ungreased wheel" (-10% movement).

Other modded features might be a cash boost if you slay an enemy "train" in battle, which would give purpose to HA skirmishers raiding civilised armies on the steppes (chuckwagon huntin').

I guess it would be a huge dislocation of the system to take such a central and interesting element as the personalised leadership figures out of the game and replace them with such a prosaic (if accurate) feature.