Stellaris: has alot of uncertainty, obviously the tech card draws are totally random, and somthing like this couldn't be used in hoi4 unless has mentioned there was setbacks when researching a certain technology but could be a kick in the teeth unless there was some feature to overcome such fallbacks at a added cost. Uncertainty features that i would advocate for perhaps being apart of HOI4 is the random world/universe generator. With a nation editor also, this could make for some fun MP/SP experiences if national focus tree could be setup to compliment a generated world. e.g ai behaviour instead of alternative storyline focusus.
EU4: Extremely fun and at times frustrating to play, the level of uncertainty in this game makes it both fun and criminal to play. But an uncertainty that could be brought over from EU4 to HOI4 is perhaps the certain advantages/disavantages events that pop up depending on what your goverment type is, your chosen nation ideas and your advisors that could perhaps be related/linked in a similar hoi4 fashion to a countries national unity, recruitment laws, economy, trade, advisors and perhaps even arms companies that perhaps ensure research doesn't fall back on certain strengths of that research company. National unity could be rebuilt within a country with a continious focus acting like a stability system to counter any events or reduce the amount of bad events popping.
CK2: Ruler/family deaths are probably the worst of all uncertainty that CK2 has to offer. Then after that vassals or council members wishing to overthrow you. I guess if they ever fleshed out the coup system a bit more, certain advisor put in position within a country to keep a certain part of the voters happy could also potentially be a trojan horse if external influence starts be projected on the country. E.g a communist leaning advisor put in position to represent the views or keep content 20% of the communist population could result in having a cooperative communist population that keep production/recruitable populace optimal but with the risk of leaking research/intel on your nation to other state actors within there area of expertise, failure to appoint enough advisors to keep a certain percentage of the voters content (e.g communist) could result in coups being more viable/lethal, or reduced productivity / recruitable populace. To give historical context, stalins great purge was to ensure all advisors were idealogs and loyal to him, & Churchill war ministry was made up of both labour & conservative MPs.
https://en.wikipedia.org/wiki/Churchill_war_ministry
To work out the balance would mean differentiating between a Democracy & Authoritarian regime. Each with there advantages & disadvantages. Both being viable to play while requiring the same amount of attention equally.
Victoria 2: Alot of victoria 2 and even to some extent CK2/EU4 felt very organic with a level of uncertainty given that alliances could change on a dime, wars to claim debt, wars over sphere of interest, ai generally frabricating claims that gave the impression of freewill, and in terms of CK2 pushing claims. Victoria & EU4 would give events for claims/war goals, but may be to much given the timeline of HOI4, but could work well in a randomly generated map. I guess somthing like Victoria 2 Crisis events which has a world power you would choose a side to force a status quo or go to war, although somewhat represented through the national focus branch could add to a more dymanic play but would probably make some of the national focus tree obsolete or create totally ahistorical showdowns that may not be favoured by alot of hoi fans. I guess that wouldn't work either since there wasn't any formal declaration of war giving for the most part, asides from the winter war & Sudetenland, but having crisis events in a randomly generated world might work.
Overall most of the uncertainty points i've listed favour statecraft & totally ahistorical setups that would be better suited perhaps for a randomly generated world with many smaller nations, to gain uncertainty in historical mode would probably be with the CK2 example i listed that can directly/indirectly affect your efforts on the battlefield, but may not be desired by some, or frowned upon in a MP game, but then, you can only fight world war 2 so many times has so many nations that kinda playtrhough the same, i kinda think a stellaris type random world generator where everyone starts of on a equal footing plus a few of the other examples i listed or not could always give a compelety different set of events and story. Not sure how difficult this is, but seemed like it was possible with
EU4 New World Random Generator, although given the amount of detail that goes into the hoi4 map atm, seems unlikely.