One motivation for HDR is having absolute physical units, such as luminance in candelas per square meter. You can imagine that might be a floating point value and that 8 bits per channel might not be enough.
The problem you’re describing is that color brightness is relative, but if you want physical units and you have a calibrated display then adjusting your brightness is not allowed, because it would break the calibration.
Another reason for HDR is to allow you to change the “exposure” of an image. Imagine you take a photo of the sun with a camera. It clips to white. Most of the time even the whole sky clips to white, and clouds too. With a film camera, once the film is exposed, that’s it. You can’t see the sun or clouds because they got clamped to white. But what if you had a special camera that could see any color value, bright or dark, and you could decide later which parts are white and which are black. That’s what HDR gives you - lots of range, and it’s not necessarily all meant to be visible.
In computer graphics, this is useful for the same reason - if you render something with path tracing, you don’t want to expose it and throw away information that happens to get clamped to white. You want to save out the physical units and then simulate the exposure part later, so you don’t have to re-render.
So that’s all to say- the concept of HDR isn’t hacky at all, it’s closer to physics, but that can make it a bit harder to use and understand. Others have pointed out that productized HDR can be a confusing array of marketing mumbo jumbo, and that’s true, but not because HDR is messed up, that’s just a thing companies tend to do to consumers when dealing with science and technology.
I was introduced to HDR image formats in college while studying physically based rendering, and the first HDR image format I remember was Greg Ward’s .hdr format that is clever- 8 bits mantissa per channel and an 8 bit shared exponent, because if, say, green is way brighter than the other channels, you can’t see the dark detail in red & blue.