Re: Ever since Rome 2, Total War suffers from a very weird paradox...
Not sure about the role the army cap plays, but the financial system is certainly a significant factor. The profits are accumulated when the income of taxation, which mainly depends on the size of the empire, is added to less dynamic sorts of income, like trade or king's purse. Meanwhile, growth means more expenses, as corruption increases, while you also need to garisson an extended front. The result is that smaller factions can afford disproportionately larger armies, which makes empires extremely vulnerable to aggressive coalitions composed of minor factors. At a certain extent, this is an accurate reflection of how economy works and ideally could provide the player with an enjoyable late-game challenge.
The problem is that, since Shogun II and Rome II, the AI really fails at economy, because it's incapable of correctly handling the limited building slots, which means that the few benefits of controlling many provinces are almost completely negated by corruption. Therefore, either its economy is surprisingly fragile or its armies can recruit nothing better than ill-trained militias. Meanwhile, the higher the difficulty is the weaker empires become, because of the enormous gifts the AI receives. This leads to the standard income, regardless of military expansion, being more significant than any fiscal revenue, so larger states have almost zero chances against a unified attack by minor parties.