The main advantage with RAW is that several of the camera's lossy processing steps such as sharpening, noise reduction and demosaicing are not yet "burned in" to the image file, allowing you to choose the algorithm later in software, and re-adjust it as many times as you like with different settings, without the generational loss associated with applying further processing to an already-processed image.

For a more technical description, see my answer to What is RAW, technically?.

Here is a list of things you have more control over in software later, if you shoot RAW:

7. Contrast / Gamma correction

   This is also where the bit depth advantage - as mentioned by the question - comes in. Linear values need to be converted to gamma-corrected values to work as an image file, and if you re-do this later you get banding. Going back to the raw data enables you to re-adjust the contrast curve without introducing additional banding.

8. White balance and colour space conversion

   If you re-do colour balance to a raster image, you can also potentially get banding or even clipping, so doing it in the RAW software can apply it based on the original raw values, along with the contrast curve (above).

9. Sharpening and noise reduction

   There are different sharpening and noise reduction algorithms, and this is a lossy procedure. If this is done in-camera, then you are stuck with whatever sharpening and noise reduction was applied by the camera. A RAW image editor can adjust these values without the generational loss associated with applying a further sharpening or smoothing to an already-processed image. Doing it in the RAW software may also give you the opportunity of using different sharpening and noise reduction algorithms or adjusting more of their parameters.

10. Demosaicing

    A RAW image does not store colour values for every pixel - instead each value is a monochromatic value measured from behind one of three colored filters in a Bayer array. However, you need each pixel to have all three colours - red, green and blue - for the final image. Therefore, a demosaicing algorithm has to guess the other two colour parts for each pixels, and it does this based on knowledge of surrounding pixels. There are a variety of different demosaicing algorithms with varying qualities, and it is a lossy process. If this occurs in-camera, then you are stuck with the camera's built-in algorithm. If you use a RAW image editor, you may be able to use a smarter algorithm, and you may have control over the algorithm used. This can affect its sharpness, the degree to which it shows aliasing artefacts, and whether it throws away the edges of the image.

11. JPEG compression

    Of course - if you are comparing RAW to JPEG, with RAW you're not dealing with an image that has JPEG compression artifacts - even before you start post-processing.