Or you could scale the image on a wrong-DPI device so that it is of the correct physical dimensions when shown. (Depending on the device's capabilities, you may lose detail.)

Yes. By embedding the dpi at which an image was recorded or constructed within the image file, it allows for the possibility to scale that image up or down to correct the size when displayed on mismatched devices. But, as you say, detaisl can get lost or become blocky as a result.

The problem is, it encourages the thinking "if I make my images at high dpi, they'll look good whatever device they are shown on", but it doesn't work that way.

If the image is recorded at 300 dpi, and then displayed on a 96 dpi device, it'll either be 3 times too big, or all the fine detail vanishes. And in the bargin, (ignoring compression), you've transmitted 9 times more data than will be used in the final display, for not just no benefit, but negative benefit.

Far better to record images at a lower dpi, that more closely matches the likely display media and offer a click to zoom facility that links to a larger image for those that need one.