That shit needs to go away. A short sword being two radically different prices is just lethal. They need to be actual inventory that you can use to equip new units. This is the whole point of having actual production. Looting weaponry is like looting resources, but you gain the actual weapons instead of mysteriously melting them all down into gold. You can end up with weapons you don't even have access to.
Once you turn them into a product, the whole game has added depth available to it. Producing units is no longer back loaded into training time, allowing build up before war to be an actual buildup instead of training units endlessly and strangling your economy a hundred turns before the fight even starts.
Loot can be more complex, refined resources being vastly more valuable than raw. Losing a key battle can turn an entire war against you as the enemy uses the captured equipment to outfit new units almost immediately, instead of 30 turns later when they've finished a ridiculous training cycle. At high retention levels, this even helps with late game slowdowns. If you're trading units back and forth in a constant bloodbath, you wont be waiting a hundred turns between campaigns after using your spoils to reequip.
Your spoils from adventuring are no longer hero centric. Once they become uniform in usage, you're not restricted to a single avenue because you researched adventuring before loading up on the arms. You can have much more interesting loot as well. An entire cache of pre-cataclysm weaponry could be found, allowing you to equip units with your unique, irreplaceable armaments.
It changes the scalability as well. You can have amazingly powerful weaponry without an amazingly long training time just by devoting more resources to producing your hard to make equipment.
In general, I agree that the difference in cost of weaponry between a champion and a regular unit probably needs to end as it doesn't make a lot of sense, but I whole heartedly disagree with the rest of your post. On this first point, I feel that all non magical equipment should simply be free for the sov and his champions. If you are the mighty king of a faction, it would stand to reason that you would have full access to the armory of your military at all times. However, the cost for a regular unit, both in terms of training time and resource cost, are abstraction of the experience of a soldier in training. The more complex the weapon, the long and more costly the training. This is fully in line with real and fantasy settings, where using a weapon takes time and experience to become combat effective.
Now, as for your larger point about looting, I don't remember that part in the Lord of the Rings, where the battle of helms deep finished and everyone went out and picked up all the weapons and then used to them to make a well equipped army. However, on a more serious note, I don't see how looting a weapon will somehow make the training times of units decrease. So if I gave someone a bow, that makes them a combat ready bowman? Or Does giving a man a longsword and some used armor make him a gallant knight? Obviously, the answer is no, as in both of these cases a trained soldier would instantly kill both of these feeble combatants with their superior training. A key, decisive battle turns a war effort due to the excessive losses by an opponent, not simply because you can now loot the corpses of the dead. Under the model, a player could sacrifice the vast majority of his army secure in the knowledge victory will secure him a significant bonus to replenishing his forces while putting a huge burden on his opponent. This is not how wars are fought, and it would simply detract from the real dangers of overextending a war effort.
I think this entire debate comes down to a simple question. Do people really want to worry about actually making weapons/armor? I mean I have played Settlers and can easily say that is not exactly fun times for me to have to build 18 buildings and manage a whole host of workers so that I can make 1 suit of armor.
This said, I think that it might be workable to allow a champion a small chance to loot a non-standard items from enemy champions. Say there is a champion/sov who has a +2 longsword when you defeat him. In this specific instance, I think adding a 5% chance to loot the item makes perfect sense as it would be a significant moment in the experience of the character.
In general, I think this particular idea about weapons as a resource would push the game in a bad direction, as it would add a significant advantage to players for victory in war, while ignoring the development of their empire's infrastructure.