I shoot JPEG + RAW because my camera produces really good JPEG output. It has flexible control over tone curves, color, and contrast. I'm not usually interested in producing HDR-compressed images — in fact, I often prefer a high contrast look which reduces dynamic range. If I get the exposure and other settings right, I really don't benefit much from RAW.
If I make a mistake with white balance or am in a tricky situation, I have the RAW file to take advantage of. Most of the time, I develop that in-camera, using the built-in tools to do so, but in the cases where I'm not satisfied with that, I use RawTherapee. (My camera allows adjustment to the color of the LCD; it's not completely color profiled, but it's basically neutral, so I can trust my eye well enough.)
I know that some cameras only allow highly compressed "Basic" JPEG in combination with RAW; mine lets me save JPEGs of any quality, and in fact, I usually use ★★★, only increasing to ★★★★ when the scene needs it or when the image appears particularly special. (See Is it worth using the Premium JPEG quality setting?)
And, in fact, in the interest of keeping my lifetime data load sane, I only keep the RAW files for those particularly special images. I know this is verging on sacrilege against the conventional wisdom, but I haven't regretted it yet. If I had paying customers, I'd definitely archive it all, just in case.