Just to add to this given I have finally got around to reading Daniel Todman's Britain's War:
'At the start of 1941, it was calculated that each division of 18,000 men required another 23,000 soldiers behind the lines'
Maybe this sort of ratio is what could really eliminate spam.
I think some kind of logistics rework and upkeep as you mentioned should be part of the solution, but the issue goes beyond that.
With the current system, as long as the AI has free manpower, then it will just keep pumping out more and more divisions. It has no concept of keeping a reserve of manpower to tap into for battlefield losses. Still less does it have any concept of living within its means as far as outfitting divisions with equipment and replacing battlefield losses of equipment.
It does seem like there needs to be some sort of 'upkeep' which makes going beyond a certain number of divisions(no doubt influenced by your economy and population) deeply undesirable and which the AI also respects. Simply increasing the manpower requirement of divisions to reflect logistics won't actually change that issue, plus there's an issue where if you increase the manpower of a division it will take more losses. This is not good considering losses in combat are arguably already too high and the logistical people shouldn't be on the front line fighting in the first place. There will need to be some kind of comprehensive rework to how divisions in the game work and are implemented by Paradox to allow for non-combat manpower to be represented well.
I'd agree with The Me In Team that it is *mostly* an AI issue. It isn't entirely because it's very easy to make a large number of garrison divisions that will not ordinarily see combat, and there is currently no cost to this other than the opportunity cost of not having directed that IC towards combat divisions/materiel. Given how much the games combat system stacks things in favor of the defender, especially when we're talking about amphibious invasions, there should be more than simply an opportunity cost to maintaining massive coastal garrisons. There should be an actual material cost that is beyond the simple opportunity cost of having X number of rifles, support equipment, and artillery sitting on a stationary division.