Dude, I gotta call abuse of the term "objective" on you.
"Fun" is subjective, right? So the statement "add complexity without adding fun" must be subjective.
Actually, I think it's more valid to call abuse of the unqualified term "fun." I'm not trying to quibble about individual word usage, but I did leave that vague.
There is some game design that just is not as good as it could or should be -- and by this, I probably mean "it does not well serve the purpose for which it is intended, or it slows down the game excessively, or it prompts repeated arguments and confusion due to the way it is designed or presented." If you're actually looking at "fun," I think it's fair to use a shorthand metric of "what a preponderance of reasonable people would think after comparing the two."
In 1e AD&D, how many times did you use the grappling, pummeling and overbearing tables? Go play out a 1e bar fight using these tables and no weapons, then do the same in any version of D&D from 3e on*. Which do you think ran more smoothly, which was easiest to learn, and which do you think was a better emulation of a bar fight?
Or 1e psionics. 1e psionic combat between two psionic characters took place at one attack per segment, not per round, so 10x faster than normal combat. That meant that every other player sat there and waited, and waited, while the DM and the one psionic player scanned through charts for 10 subjective rounds. That was probably fun for the player of the psionic PC, but I can't objectively call that good design.
If the purpose of a game is complexity, if that's the actual goal, then a complex system that meets the goals is probably objectively good and leads to more fun than a simple system. I have trouble of thinking of many games where that applies, though. How many games have "confuse and frustrate the players with poorly organized minutiae" as their goal? I'd argue that most games should be only as complex as they need to be to in order to reach whatever that goal is. In 1e AD&D, the point of initiative is to see who goes first in combat. It's not a mini-game, it's not a fun bonus challenge, it's a tool -- and thus, if it isn't clearly and unambiguously accomplishing its job it's not a well designed subsystem.
EDIT: one last note. When I say "reasonable people," I think it's good to look at the intended target audience. I'm not going to decide that a super-complex Avalon Hill board game is poorly designed if I'm comparing it to Hungry Hungry Hippos. I can make determinations of what mechanics work best for speed of play, clarity/intuitiveness of rules understanding, and for accomplishing the game's actual goals, if I compare two similar war games.
* except for 3e grappling. We played 3e from 1999 to 2011, and it was
still a pain in the ass to remember. But I digress.