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.
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.