This post pretty much lays out a facet of what I love and alludes to the bigger picture: start with a historical setting and run with it, often diverging.
One game I became the king of Ireland and then somehow the king of Britanny. I then only had female child heirs. They got overthrown and ended up cast out of Ireland.
I was intrigued by that so I started a game as a count in Britanny. Worked my way up to the petty king of Britanny. Somehow engineered inheritance of another duchy - became a proper king of Britanny and then somehow became king of Aquitaine (so the king of half of modern day France).
EU4 is another fantastic game based on the same engine. Less focused on dynasties and more geopolitics/colonisation, this also throws you into historical settings. As Portugal, I became holy Roman emperor - they got into a fluff where no one liked each other so I was the only choice even though I wasn't in the HRE.
I'd love for Paradox to officially "link up" all the games so you can go from ancient Rome all the way to say the modern world. That would mean EU: Rome and Victoria on the new engine and also a new cold war era game they definitely need to make (focusing on modern geopolitics).
Clearly a secret Paradox fanboy!
The point about historical divergence is spot-on; a lot of the fun is in having some familiarity with the way things actually turned out, and comparing it with whatever ended up happening. During lulls in activity in my own kingdoms, for example, it's enjoyable just to look around the map and see what the heck is going on elsewhere.
Speaking of alternate history, I recently started getting into Hearts of Iron IV (which takes place during WW2), but actually have been getting a lot more enjoyment out of the mod "Kaiserreich" instead of the base game. Kaiserreich is an alt-history mod where Germany wins the First World War, and so by the time the game starts in 1936, the world is already quite different-yet-familiar (the US on the brink of a second civil war, France and Britain taken over by syndicalist revolutions, the British royal family exiled to Canada and attempting to retake the Home Islands, etc). Definitely recommend looking into it, if for no other reason than to read the lore on their project wiki ( http://kaiserreich.wikia.com/ ).
I've also thought about how interesting it would be to link up the Paradox games, and there are importing tools that kind of do the job, but having everything in a single game would be hard to achieve and still have the deep complexity that we enjoy. Modelling the feudal world of medieval Europe is fundamentally different than the nation-state-focused world in EU4 a few centuries later. I fear that any attempt to merge the two would end up like the Civilization games, which achieves a start-to-finish continuity but at the expense of losing a lot of interesting detail.
By "link up", I didn't mean the same game. I meant something like a save converter that takes your CK2 save and you can use it to seed the world in EU4. Then it's just a case of doing that up the chain and filling in gaps with new games (I believe timeframes of CK, EU and V sit back to back).
These games are not for everyone. Also, not entirely unlike Dwarf Fortress, they might seem a bit off-putting due to their complexity. But they have a much better GUI, and learning the basics is faster. It still takes time, though.
People loved it with CK2 because it expands the game so much, and it was unlike what they were doing before. This helped people forgive the fact that the base game was just okay at launch. Contrast that to HoI4 where the base game was not fantastic at launch (but probably not much worse than CK2 at launch in terms of stability and systems) and then the DLC train started and I saw a lot more negative comments online. There were similar conversations around the Stellaris launch "Oh they are going to make us pay or features that should have been in the game in post launch DLC".
That could just mirror changes in players being hyper-sensitive to DLC/Monetization strategies these days, and probably don't bother the people who are really into Paradox games and put hundreds if not thousands of hours into them.
I am very interested to see what they do next with Crusader Kings, since they have mentioned a few times they plan on ending the DLC soon. Transitioning to a CK3 seems incredibly difficult given how barebones it will feel.
After a Paradox game, although fun, Civ just doesn't cut it.
Which is not to say I wouldn't love to see it happen, but it's a hard problem.
Because they're so moddable, a total conversion would be possible. I know the mechanics are similar but the game of thrones mod is breathtaking (I recommend this too)!
A good place to start would be the time when Rome was merely a small kingdom and take it from there. Lots of Mediterranean based conflict with other civilisations like the Greeks, Egyptians, Estruscans, Carthage, etc. The end result might not even be a Roman Empire but, however unlikely, a Gaulish empire or a Carthaginian empire. That sounds like a lot of fun.
"Friends, countrymen. The rampaging horsemen of Kirghiz have long plundered the world and burned down cities and used the bones of our fellow Christians to fertilize their fields. We have heard from our friends in Gotland that Kirghiz intends to do the same to their houses, and we shall prevent this. Sound the alarms, muster the levies!" Two months later: "Er, never mind, Gotland surrenders." And a month later, "Friends, countrymen…"
Beyond that, it can be fun to watch just how screwed up the game can get sometimes. I had one playthrough where the Kingdom of Andalusia was located in Hungary, the Kingdom of Africa in Italy and the Kingdom of Italy in Africa.
http://steamcommunity.com/app/42960/discussions/
It appears to be still for sale ($20), without overwhelming reports of technical issues:
