I think before we make big changes, we need to review some aspects of how things are now.
1. Not all armies are derived from pops: consider clone armies, mega warforms, xenomorphs and so on. It's not clear how these would factor into an army cap. Also, some armies are far more powerful per army than others; does that mean they should also use a lot of capacity?
2. For what it's worth, quality already matters a lot more in armies than it does in ships. With ships, it's nice to have better weapons but ultimately it's all about the aggregate amount of fleet power, whether that's a few good ships or a lot of mediocre ships. With enough of an advantage over your opponent, you'll take limited losses too, because the combined firepower of that mass of ships is enough to annihilate whatever comes into firing range (and actually weapons range is the only "quality" stat that can't be completely negated by quantity). Planetside though it's not like that, because combat width is a thing. If you try to assault a Fallen Empire homeworld with nothing but basic armies, you can win eventually but it's a giant meatgrinder and you end up consuming several times as much army power as the defenders' power, because you can only use a small amount of your power in each wave. Conversely, if you assault planets of a regular empire, even planets covered in fortresses, with Cybrex warforms, the defenders are just helplessly mown down almost regardless of their number, and your armies can keep assaulting planet after planet while taking next to no damage.
3. There is already a cap on how much stuff you can expend in a war, namely war exhaustion. There's no manpower per se, and the mineral cost of spamming out armies is indeed pretty negligible by the mid-game. However, if you throw away enough armies in a single war, you'll hit 100% war exhaustion and be forced to peace out. (This is not uncommon in the aforementioned "human waving the Fallen Empire homeworld" scenario.) There is even a scaling factor, where different kinds of army cost different amounts of war exhaustion.
The obvious weakness of war exhaustion is that it's per war, not per empire, so if you're "exhausted" out of one war you can immediately go start another war with someone else. Maybe there should be something that carries over between wars to reflect a limited capacity for aggression (depending vastly on empire type, e.g. obviously a Determined Exterminator should take a lot longer to get tired of war than some random non-Militarist non-Gestalt empire that happened to build a Colossus). But I don't know if manpower specifically needs to be modelled, or if there is even a consistent way of doing so across all empire types and army types.
