That’s not why we use RAW. It’s partly because (1) if you used Adobe RGB or Rec. 709 on a JPEG, a lot of people would screw it up, (2) you get a little extra raw data from the pre-filtering of Bayer, X-Trans, etc. data, (3) it’s less development work for camera manufacturers, and (4) partly historical.
No - the non-RAW image formats offered were traditionally JPG and 8-bit TIFF. Neither of those are suitable for good quality post-capture edits, irrespective of their colour space (in fact, too-wide a colour space is likely to make the initial capture worse because of the limited 8-bit-per-colour range).
These days there is HEIF/similar formats, which may be good enough. But support in 3rd party tools (including Adobe) is no better than RAW yet, i.e., you need to go through a conversion step. So...
Another advantage of RAW is non-destructive editing, at least in developers that support it and are more than import plugins for traditional editors. I rarely have to touch Photoshop these days.
Try adjusting a 8-bit RAW file and you will have the same problem.
You are conflating format and bitrate.
The actual main thing about RAW is that the transforms for white balance, gamma, brightness, colour space, etc. haven't yet been applied and baked into the file. With JPEG, at least some of those transforms have already been applied, which then limits how mucn you can do as opposed to starting with the untransformed sensor data.
You could definitely do much more with a 12-bit JPEG than you could with an 8-bit JPEG, but still not as much as you can do starting from RAW data.
A simple example is white balance. The sensor doesn't know anything about it, but typical postprocessing makes both a 2700K incandescent and a 5700K strobe look white. A photographer might prefer to make the incandescent lights look more yellow. There's a white balance setting in the camera to do that when taking the picture, but it's a lot easier to get it perfect later in front of a large color-calibrated display than in the field.
Another example is dealing with a scene containing a lot of dynamic range, such as direct sunlight and dark shadows. The camera's sensor can capture a greater range of brightness than a computer screen can display or a printer can represent, so a photographer might prefer to delay decisions about what's dark grey with some details and what's clipped to black.