Let's clear things up a bit.
AIGLX aka. Accelerated Indirect GL for X:
It's an X server extension that allows a graphics driver to accelerate indirect GLX calls and thus have a GL application running server-side rather than client side. Normally when you draw you want to use Direct rendering and what happens there is when an application loads libGL.so, it will ask the DDX (2D X driver) what 3D driver to use, and load it. libGL will then effectively write directly to the graphics card. With indirect rendering, the GL calls are sent over a socket to the X server. Since compositing managers are run server-side and more or less hooks windowing calls, it makes sense to use indirect rendering.
Why don't we have it? because OpenGL ES is not OpenGL and thus we don't use GLX, nor do we use AIGLX.
Compositing (Compiz, KWin, Metacity, they can all do it):
Why do we want it? The X.org people have long been talking about having a "composited by default" environment. Why? Because compositing is both theoretically and practically faster than non-composited rendering. When using compositing in the X server, you can speedily move windows on the screen as what was once a painstaking amount of redrawing with a single buffer has been split up into many small buffers that don't need to be moved and can snappily be redrawn with the sheer awesome power that is the GPU. Even without a GPU, PCs are fast enough to do this with the CPU alone and still maintain a pretty smooth interface.
Remember when you tried Compiz on your PC a year ago using a radeon card and it just completely fucked up on all GL related things? That was a remnant of the old system that has luckily been completely eliminated by now (granted you have a KMS enabled kernel).
Plasma:
Now I've no idea why anyone would bring up plasma in this discussion but please tuck it away. Plasma is KDE's new way of making the experience a lot prettier, but it has nothing to do with compositing. All plasma is is a collection of widgets and widget-APIs stored in the form of HTML, CSS and some JS, exactly like Dashboard Widgets for OS X, with the API side being in JS, C and a couple of other languages. The plasma rendering takes place in WebKit and is then displayed onto the desktop rather like a canvas. The panel interoperates with the desktop which allows you to move the widgets between the two but plasma can render all its effects with or without compositing enabled.
What would be really cool:
If we could have a compositing manager with nothing but smoothing effects written specifically for OpenGL ES. The problem is we can't. Any compositing manager to achieve some sort of decent speed needs GLX 1.4 and AIGLX to render its content without duplicating an assload of things. So we're basically screwed. Also, the driver provided to us by TI is of course closed source, so we can't actually add this feature.