There's something to be said for keeping them apart... but allowing more complex political dynamics would, IMO, do a lot to make the game more interesting.
Supposedly it's just supposed to be a war game, but the war in this game is less detailed than any other Paradox game, CKII included (this arguably not being the case now that strategic forts are a thing, but that's the only manner in which it beats out Vicky or CK). The real strength of EUIV is the combination of warfare with diplomacy and true grand strategy - thinking about things beyond the confines of immediate conflicts.
Adding limited complexity to the political dynamics of each state would not only give us something more to do when where we're fiddling our thumbs waiting for truces to end or for opportunities to present themselves - it could greatly enrich the diplomatic game in general.
We don't need anything on the scale of CK2 or even EU: Rome. You could make do with ~10 characters per realm. For example, in a monarchy, the characters would include the ruler and his immediate family (parents, siblings, spouse, children, with visible children per ruler limited to 2-3, which will also limit visible siblings upon ruler shifts). Each adviser would also be a character, and you would always have one of each category. You could swap between them as you can now, the difference being that you only have to pay their upkeep if you want to get their bonuses (maybe we could also get an option to pay them at different tiers, i.e. we have a level 3 advisor that gives discipline, and we can choose to pay him as a level 1 advisor and only get 1 monarch point... but that's a suggestion for another thread). This would allow situations with characters like Richelieu actually having importance beyond giving you lots of monarch points.
This presents many opportunities to make diplomacy, and espionage, much more interesting - the main point of it wouldn't even be internal management. Royal marriages and planned inheritances would be harder to fulfill, but also more logical - if a union happens, you will have personally set it up. Espionage could involve bribing individual characters, or supporting a brother's claim to the throne in a pretender war. We could also have events for more capable relatives to pick up the slack for a crappy monarch, provided that we're willing to part with legitimacy, or risk a brother or son desiring the throne for themselves.
And it would all be generally manageable, because you would never have more than ~10 characters per realm, and the only ones that uninvolved parties would have to worry about would be the 1 or 2 potential heirs. The game would remain about international diplomacy and grand strategy, and this would in fact make these aspects richer.
