There are a few factors in the more common use of what, as has already been described in this thread, is known as stylised visuals. The single largest factor is simply the industry's shift to mainstream entertainment, and the search for increased profit margins.
The first primary reason is simple performance. Realistic rendering of light, shadows, particles, models, textures and so forth has some very large system requirements. By lowering the complexity - such as that of a stylised art design - you also lower the system requirements. This ensures that your game can run on a host of machines, and thus increases your potential market.
The second primary reason is that of the cost of content creation. Making enemy models for id's Rage, for example, is expensive. Very expensive. Animation, Textures, Bump Maps, A.I., etc. It's not cheap to make AAA quality content. By using a stylised art design, you can lower the cost of production of the content for your game. Instead of 150k polygon models, you can use 15k polygon models, decreasing contruction time considerably.
The third primary reason is that of standing out. World of Warcraft's Art Design made it standout upon it's release; since then, we've seen it immitated in every conceivable genre. Now, Publishers are looking at ways to make their product standout from the pack. One way to do this is simply use a different art design. Look at Borderlands, for example. The original art design was a gritty, very realistic one. The one we have now is something unique, distinctive. People remember Borderlands.
The last reason, and the least used one, is simply artistic direction. Chosing an unique art style to match your game design, lore, characters, setting and story is the primary method for helping mesh the entire chaotic mess of a game into a perfect, unified whole. This is often neglected; few Publishers allow their Developers the freedom to do this; it's either Call of Duty Realistic or World of Warcraft Cartoon - these are the proven sellers, so mimicking them is safe, secure and trust worthy.
I'll end this with an example of how Art Design can make your game distinctive, memorable and incredibly unique and fresh...
... and also completely alienate the mass market, and thus cause it to be shunned by consumers.
This is the game 'XIII', released for the PC and Original Xbox. It didn't sell very well, however ask anyone who played it: it was memorable, fun and a damn fine game.
