You're misenterpreting historical facts to come to the wrong conclusion, especially when comparing it to how "well" EU4 models it. I've not read the books you and other people read, but logic dictates this:
Yes, in neutral and relatively fertile and rich territories an army that was granted (or simply took) a right to pass through had probably an easy time to buy supplies. This was, I assure you, not the case in regions plagued by famine, war or simply really inhospitable terrain like deserts or high mountains.
If your army was routed, though, there was a high chance that your treasure train was taken as well. Suddenly, no more money to buy supplies. So soldiers have to resort to plunder. Numerous descriptions of battles mention this, numerous cases document the anger and fury of local rulers and population about soldiers plundering lands they were granted free passage in.
Then you talk reinforcements. Sure, in many cases, local people, local lords, sometimes foreign lords, joined the ranks of an advancing army. Either for personal glory, money, to escape ciminal prosecution, hatred for the enemy forces and nobles. Just as many people joined these armies as non-combatants, to provide services (scouting, translating, prositution, repairs, cooking etc.). Yet after humiliating defeats, most of these deserted.
You can't put forward what you describe as rationale for EU4 if EU4 doesn't model this.
- non-belligerent provinces that you pass through don't profit from your purchases nor suffer devastation from your looting.
- provinces you pass through don't lose the manpower that you gained.
- you don't lose professionalism when recruiting foreign fighters (which should be, realistically, treated as mercenaries)
- if you lose a battle, the exact opposite of historical fact happens: while you retreat, you gain *more* manpower, you *gain* morale, money is readily available, no looting happens.
- in hostile terrain, you gain manpower from thin air. Sure, you could claim (validly) that this manpower coming from people and nobles in the foreign empire willing to join your cause. Yet this manpower is not substracted from the enemy's manpower pool. You could argue that this taps into a special part of the enemy's manpower that isn't available to him. But neither does it model that these people are perhaps fighting for something
they want from this war. For example higher autonomy or independence for their provinces. And why would anyone join a penyless retreating army is beyond my understanding.
Historical fact tells us that in big international wars at least, big battles were critical. If you lost a critical battle, the war was basically over. In many cases, it also involved controlling critical forts (sieges), sure.