But then smaller kingdoms still wouldn't be able to keep up with bigger ones. Because smaller kingdom will usually mean smaller economy, and therefore less gold and less research. I'm not saying the larger kingdoms shouldn't have an advantage, but this 'double win' could easily unbalance the game.
How do you think it as a double win? If the army size was a linear progression, then the large kingdom's economies of scale would outgrow the upkeep demand of their increasingly growing army - that would be the double win. They'd get both a bigger army, and a much stronger economy. But doing upkeep like this (I'd possibly even have N be a percentage, rather than a flat amount, but haven't done any testing with math) means that yes, the larger kingdom does have the economy to have a larger army, but it has to sacrifice much of it to do so. If done correctly, that means even though the small kingdom is outmatched militarily, it can still sort of compete economically.
Also, it promotes de-stacking when there are no enemies around, and only re-stacking when you plan to attack or fear you will be attacked. This adds a lot of busy work IMO.
I just assumed it was global, not per-stack. I'm not really harping on the number being 8 since I'm pretty sure it's just a random example number to demonstrate, and not the exact proposed change. Kind of makes sense since it's research based, your kingdom gains the infrastructure to field and effectively command an x number of army units, and everything above that needs greater investments to remain effective (turning into the "extra" upkeep beyond the basic soldier pay)