Yes, but why can’t the camera do it continuously? Film at 240fps and provide a 60fps output with 10bit color depth.

Because the images would look funny. Imagine you're capturing someone running - at frame 1, they would be at position x, and at frame 2, they'll be at position x + 1. If you try to stack them together, you'll get a weird ghosting effect.

Well, that ghosting effect is also called motion blur. If I integrate continuously, that is.

Motion blur, but different parts of the image would be exposed differently due to the nature of HDR, resulting in an odd look. Imagine instead of a runner, that you're panning from a dark to light scene.

Not necessarily.

Assume we say an 8-bit image is taken every 0.1 second, if I merge 4 of them, wouldn’t I just get a 10-bit image with 0.4 second shutter time?

Because I essentially just take the RAW image, load them into a 10-bit colorspace, add them up, and then store the image.