I don't hate the idea of a "supply line" sort of support for units. But I would keep it as simple as possible - maybe units take one food from your closest connected settlement, if within X tiles. Otherwise you take a hit of 2hp per turn or something. Maybe you double it (and your regular unit maintenance) in enemy or occupied territory? Then you could legit bring back the "supply convoy" as a unit that acts as like a range extender for your army. That would also give a little extra penalty to trying to conquer the entire new world while your only non-occupied settlement is a dinky fishing town. You'd have to pillage to feed your troops then.
-"keep it as simple as possible" haas to be the absolute basic rule for any 'supply line' mechanic. It is far too easy to make such mechanisms become completely overwhelming in complexity until they make the game - whether board or computer - a chore to lay and Not Fun at all.
So, extending on your post a bit:
Supply Sources are either dedicated Supply Bases (if we want to include them at all, and then I suggest only in Exploration and later Ages) or friendly Settlements. Within X tiles, a friendly Settlement can supply as many (military) units as it has population points.
Distance X would vary depending on roads, terrain, and technology (Age) and possibly cpould be extended by Supply (Trade?) units, which would be hideously expensive in Antiquity but cheaper in Exploration and relatively cheap but fragile in Modern Ages (as in, they could be attacked by Air Units and destroyed, putting your units suddenly Out Of Supply)
Units out of supply take damage as if they had been in battle. The exact amount of damage depends on the situation. Units 1 - 2 over the supply capability might take only 5 - 10% damage per turn out of supply, but that percentage would increase if they were in Hostile territory, or inherently Unsupplied Tiles like tundra or desert. Units out of supply long enough, then, could be completely destroyed by lack of supply: starvation takes no prisoners.
The supply capacity of a settlement can be increased by having trade routes between it and other friendly settlements. In Antiquity and exploration, ONLY sea trade routes count for this, and each friendly settlement connected by a sea trade route adds 1/2 of its population to the capacity of the settlement supply source.
BUT also note that sea trade routes between settlements of your own empire don't actually add any other 'trade benefits' in the game, so that providing near-infinite supply to a base for a campaign will take away resources from your economic trade routes to other empires/IPs and very neatly show the trade-off required between 'guns and butter'.
Naval units in Antiquity or Exploration require no supply: ancient galleys foraged for food every few days and Exploration sailing ships were remarkably independent of constant supply from Home in their voyages. The most that might be required would be for Modern Age ships and any earlier Age Naval Commanders (Exploration Fleets) to require supply from a friendly Harbor settlement, but the supply range would be much, much longer than any land route.
Everything else is extra. Modern Age units that require oil to move or massive tonnages of ammunition to fight might require some extra supply rules and penalties, and 'special' supply rules for units that almost inherently do not require much supply like light infantry or light cavalry might have percentage supply enhancers, but none of that is required - and this is one place where the Age Distinctions can work for the gamer, making it easy to distinguish between largely self-sufficient (foraging) Antiquity and Exploration armies and Modern (Age) armies with massive supply requirements.
