Complexity is a good thing. Indeed, it's one of the best things, maybe the best things there is. If we tweaked the fundamental constants of the universe such that the universe was made of nothing but hydrogen atoms, it would contain the same amount of information but none of it would be complex.
Sorry, but you are incorrect here. It takes significantly *less* information to describe a universe that is all Hydrogen than our universe. I our universe, to describe things within it, we have to describe where it is, how it is moving, and what it is. In the all-hydrogen universe, we don't need to know what, as that is the same for all things, vastly reducing the amount of information within the universe.
And, here's an interesting thing to chew on - one of my possible thesis projects was in what we call origin of life calculations, which includes study of self-organizing systems. We considered the probability of a system going from just a disorganized collection of molecules (a condition of high entropy) to an organized collection of cells/organisms (a condition of much lower entropy).
If your system has too few different puzzle pieces to work with, you don't have enough variety, and there's nothing to organize around. If your system has too many puzzle pieces to work with, it never settles into organized patterns, as there are too many options. Life requires some complexity, but not too much. There need to be some limits on complexity for the system to be organized enough to be useful.
Make of that what you will.
I think I mentioned this in another thread recently, but it might be useful here, as well. Most folks use "complicated" and "complex" mostly interchangeably. There are times when narrowing the connotations can be useful.
We say a system is complicated, when it has a lot of different parts in action. We say a system is complex when the results of the action are difficult to describe or predict.
So, a mechanical wristwatch is complicated, but not complex. There are many parts, but their resultant overall action is easy to describe, and works very predictably.
But, we can take a much simpler system - three planetary bodies moving under their mutual gravitation (a "three body problem") is super-simple to describe the parts, but their resulting action is, in general, chaotic, difficult to describe or predict in the long run. It is not complicated, but it is complex. Or, the game of Go - the rules are not complicated, but the resulting play is very complex.
In this sense, we probably all want our games to be complex - the results are not easy to predict, there is unforeseen emergent details or behavior. But some people want this to come from complicated rules, and others probably want rules that are not as complicated.