I've discussed the relationship between simplicity and depth in my article on depth, so here I'm going to discuss other reasons why complex rules are undesirable. Simlicity has several ancillary benefits:
Reduced learning overhead. The more complicated your game's rules, the longer the player has to spend learning those rules before they can even begin to play for real. In a game that has a simple ruleset and gets its depth emergently, like Go, you can spend less time learning the prerequisites and more time enjoying the game. But this is pretty small for someone who's going to learn the game either way and end up playing it for a long time.
Accessibility. Obviously the easier to learn your game is the more people will be motivated to pick it up. This isn't really a factor of the objective quality of the game, but it certainly is important for success.
Balance. More complex games are harder to balance. If there's more game elements or more rules, it'll be harder for the designers to anticipate how they might interact and prevent degenerate combos that could trivialize the rest of the game, lead to insufferable stalemate situations, et cetera.
If there are too many mechanics or game elements involved in a single match, you may end up with players sticking to just the ones they know and not learning the others. I've experienced this most notably with Starcraft. I've played both Starcraft 1 and 2, and in both of them I had a problem: there are too many units! What do I do? No problem, just find a few that I like and use those every game. And that was what I did.
Despite playing ladder as Protoss in Starcraft 2 for a couple months and ranking up considerably, I don't think I ever once built an Archon. Or an Observer. Mind you this was original Starcraft 2, not the expansions where they add more units, and that's with concentrating my efforts on just one race. I was able to do reasonably well in competitive play (or so it seemed to me) without really knowing any of the Protoss units except Zealot, Stalker, Sentry, and Immortal (I might've used Carriers occasionally), so I never touched the others. The depth of the game was being lost because there was too much to learn and the game trained me to play without using it all.
I also experienced this when I briefly tried out League of Legends. Besides the gamestate information, I had to be familiar with four different abilities and too many numbers and stats everywhere to keep track of and when I went to the item shop, I gave up and left because by the time I could have read even half of those items my team would have lost the game. Not to mention how there's like a hundred different characters to play as and they all have different abilities. This created a problem where I wanted to know the lore behind the characters to pick one I liked (and since there were so many I knew there had to be one I would like), but after spending like an hour reading bad stories on their website, I realized any other game would be more fun than this.
The way Prismata and Dominion handle their large number of game elements avoids this problem beautifully. But that's not just a trivial rule change you could make to a game like Starcraft; that's a completely different core design.