You can change the white balance of a jpeg file. (I don't know why people say you can't.)
JPEGs will always contain less pixel information than an accompanying raw. They're 8 bit, they have their limits. It's a lossy format. Raw files contain a great deal more information about pixels so that when DO adjust things like white balance, you may pull in tones that are no longer there in the jpeg file.
Because RAW gives you a lot more to work with, it's a safety net of sorts. Even a high quality JPEG will sometimes clip highs and lows that are preserved in the RAW file. You can't recovery them from the jpeg.
You can't save things back to raw, however. Bridge, lightroom and ACR and all give you the ability to nondestructively apply a template of changes to each raw, but they're saved as a separate set of metadata instructions on what transformations to apply to the raw file when it's pulled into an editing program. You can save them into lossless formats, though, but even TIFF or PSD or XCF, if you've imported from the raw, you're going to lose bits of information (chances are you won't notice, ever, though, esp with the native data formats with the higher-end editors).
Jpegs however apply their compression algorithm each and every time they're opened and closed. The more you open and close them, the lower quality they'll become. They'll block up, they'll start to look horrible.
My workflow and my thinking demands that once a jpeg has been set out into the wild, I'm done with it. I never open it again. It's the last step. Do everything else in some other format. If I need to make a change, go back, and make another resultant jpeg.