Concerning supply: it's not as simple as you are describing and is-in fact- as you suggest it should be.
There are basically 2 types of supply: food and bullets. Each unit has it's own small supy of both. Units can collect FOOD from a province they are in and any adjacent. The amount depends on the development of the provinces, weather, enemy control, etc. easy right?
But AMMUNITION...Bullets, can only be resupplied by depots. A unit needs to be in a province with a depot or In an adjacent province to get supply. So you can't make your way through the countryside fighting and marching without building a NETWORK OF DEPOTS
Depots do two things: give you ammo and give you replacement troops if available
You can also bring supply wagons with you. Wagons carry a lot of ammunition and food. They will "fill up" with food as they pass through regions just like units...they can just fill more. Same with depots. So an army without wagons has enough ammo for 2 battles basically. But throw a couple of wagons in that army and you can get 4 or 5. PLUS, you can send wagons back to the depot to resupply
So, the system you describe - scavenging- does apply to food. But ammunition must be supplied through a chain of depots
This is the system used in some other AGEOD games. Others use cities as manufacturers for ammo and depots "push" supply out. That is used on more complex AGE games