I work in QA for a different game developer. There are obviously more than just the three options you've listed, but let me just tell you how QA generally works during the development process, to debunk a lot of the negative perceptions in this thread.
Ok, so we have a game, and the company determines that there is a market for additional content (DLC). So the developers need to create that additional content and add it to the base game. During the development process, QA will test basic functionality of the new features while they are being put together. It will be buggy as heck, but the goal is to get it up and running and in a semi-workable state. We expect there to be bugs... sometimes lots of bugs. Once the key criteria of the functionality works, then QA will bug all of the polish issues like alignment, wrong tooltips or whatever else makes it look unfinished, ad hocing around the feature to simulate a normal user experience.
Now, once all of the new features are added to the game, and all of the patch's main bug fixes are included, QA will run a checklist of key functionality FOR THE WHOLE GAME, including new features. Checks include things like:
[ ] User can declare war
[ ] Allies are correctly called to arms
[ ] Attrition is calculated properly
...etc, etc
Notice how I included a check for attrition, which as Arumba discovered after El Dorado was released, was completely broken. When someone from QA goes down the checklist, they would probably just check to see that units can take attrition. They don't check EVERY possible scenario involved with taking attrition, because the checklist would take forever if that was the case. The purpose of the checklist is to ensure that nothing is majorly messed up. Unit took attrition? Check, moving on. Unlike Arumba, they won't be sitting there for 8 hours with a calculator and spreadsheets deducing exact numbers and expectations from every angle. That's just unrealistic.
Bugs are often the knock-on results of other bug fixes or feature evolutions (such as making the disaster system more transparent). As we see from every patch, the EU4 devs fix a lot of bugs. Combined, there is a huge potential for small things to slip through the cracks; the slight changes here causing unwanted slight changes over there. No QA team on the planet could find everything that eventually pops up after release. Even the "bigger" issues. After one hour of release, the user base has already clocked on more man-hours than were put into the entire development cycle of the DLC/patch. And QA is only a fraction of that cycle.
Recall my explanation of the checklist earlier in this post. Notice that I said the checklist is only run AFTER the features are added and the old bugs are fixed. So the build is theoretically ready to be released at this point. The devs throw it to QA to check at the end of feature development. I don't know how release dates are determined at Paradox, but I suspect, like most companies, they are decided well in advance. Management tells the devs, "Hey, have all these features done by this date or we won't make any money". Then they tell QA "Hey, make sure this is ready to be shipped by this different date, or we won't make any money". QA takes the build after feature development ends, runs their checks, and every time they find something, tell the devs "Hey, this is broken, we need it fixed before our release deadline". The devs fix it and QA checks that it is fixed. Rinse, repeat.
Unfortunately, sometimes there just isn't enough time to fix everything. The queue of bugs will be too large to fix before the deadline. The major known issues get prioritized, and the minor ones will be fixed in the next patch or even hotfix.
The dev multiplayer sessions have their own usefullness. They simulate actual user experiences, where some of the more annoying issues can crop up. Simple checklists miss such issues, because they don't look at the game as a whole. The granularity of checklists hides bigger issues. I'm glad Paradox utilizes both.
Ultimately, from an outsider's QA perspective, I think a lot of the hate directed at Paradox after patches is unjustified. The devs are obviously engaged with their project. And the small QA team have an almost impossible task in ensuring the quality of a game which exists in a niche market with a massive feature complexity.
If anybody expects the patches to go smoothly, they're kidding themselves. I don't begrudge the developers for releasing when they do. It ensures new content comes out more regularly. Consumers-as-QA isn't ideal, but let's be realistic in this situation.
Bravo EUIV devs
Bravo EUIV QA
I know what it's like, and you are doing fantastic. Keep up the good work, and I look forward to what comes next