Events are, generally speaking, bad. They are something you learn to live with as a player, but they never really add to the enjoyment of the game. My first EU experience was in EU3, and I save-scummed every single bad event for the entire campaign just because of how annoying it was to be slammed with random effects like that for no discernible reason. I stopped doing this, but only because doing that much save-reloading was killing my desire to continue playing at all.
Specifically in EU4, events have the following design problems:
1. Many events are conditional upon doing things like having certain religions or idea groups. Because event lists are hidden, that makes many consequences of your decisions unknown and invisible until you have memorized the events or if you are cross-referencing master event lists on wiki guides. This is the worst kind of guide-dang-it problem.
2. Related to the above, event balance is kind of all over the place. Some events are so powerful that having access to them can influence your decision-making regarding choosing an entire idea group. Others are so painful that if you're not aware of them before you meet their conditions for appearing, you can pretty quickly nosedive your entire campaign (westernizing, over-extension). This just adds more punishment suffered exclusively by beginners, sharpening the learning curve and reducing enjoyment of your first few games.
3. You have no control over the majority of events. They are completely random. You might get several good bonuses back-to-back, or you might get several successive slams so severe it brings your nation to its knees. This is sensible for a simulation, but it's terrible as a game mechanic.
4. Many events, generally speaking, serve as a replacement for a layer or two of gameplay. Models of internal politics, dynasty relations, and most of your infrastructure and even legal system are either extremely shallow or, more commonly, nonexistent. Effects that should come from decisions made within such a layer instead play out randomly through events. Consequence-driven mechanics are the hallmark of strategic gameplay; randomness is the hallmark of gambling games.
5. Events interrupt gameplay. You must immediately stop whatever it is you are doing and deal with what is essentially a pop-up ad that comes with free MP loss / stability hits / year-long income penalties. Even if it gives a bonus, I'd rather it not be there at all; your product might be fantastic for me, but I still don't want you throwing pop-up ads at me!
6. There are many negative events, which can be major fun-killers. It's better to weaken nations in general and have only positive events than have the current baseline with both positive and negative events. The Civilization designers discovered this when they tried to add periods of decline to Civ. It playtested very poorly. They inverted the mechanic to Golden Ages, which playtested very well, and now it's a staple of the series.
Essentially, everything that events model should be replaced by a system that I as a player must seek out and interact with purposefully, and the resulting effects should be consequences of my decisions. Off the top of my head I can envision skeletal structures for three or four fairly simple management systems that would eliminate some 90% or so of the events in the game. I'm quite confident the pros at Paradox can do the same, but they must first decide that events are in fact a poor system that could use a total replacement.