For Game development, there are several advantages to the "2.5D" approach. Probably one of the biggest is animation. 2D animation takes a lot longer to illustrate and change than 3D animation. With 3D animation, you create a single base, and then you can genarate a near unlimited number of animations from any visual angle. If you want a complex character to be seen from more than one angle in a purely 2D game, it's back to the drawing board for another thirty or forty frames of animation. In a 3D game, all you do is flip a variable around.
Another major advantage is framerates. It is possible in some 2D games to get away with 12 frames per second. But if you want your game to have silky-smooth animation, you are going to want to shoot for 24 fps. And that's a crap-ton of frames for your average illustrated character. 3D animation uses keyframing and interpolation for a lot of its animating. And that means that most animations aren't tied down to a specific framerate. If your engine is running really well, 60 fps is a perfectly reasonable frame rate for them to run at.
2D development has fallen out of favor more due to inefficient development than actual player preference. The skills necessary to construct 3D models are easier to teach than those necessary to illustrate. Of course, this has also lead to the industry being awash with generic space marine 3D models.