How is that different from what photographs do?
> Furthermore, game development is a race against time. You have milliseconds to render the scene and apply tone mapping.
Maybe I know just enough to be ignorant of the topic, but LUTs are just lookup tables. People working in film apply LUTs to the footage they're watching in realtime on normal PC hardware. Fragment shaders have been common in games for years. Last year I was working on a VR project (targeting 11ms per frame) and I think the post-processing took between 0.25 and 1.5ms--any more an it would have been dropped). For a desktop game having 16 or 30ms to render many fewer pixels is an eternity, comparatively. The only difference between a LUT and ICC profile (which most OSes support out of the box) is that for ICC profiles are mean to be calibrated against either an input or output--they're used everywhere in realtime.
I've never actually used ReShade, so I had to look it up. It does way more than color correcting. Depth of field, ambient occlusion, antialiasing are completely separate from tone mapping and notoriously computationally expensive (not just in video games, but in film as well). I also think since third-parties are writing them, they're not always tuned to be performant.
A typically developed HDR photo is a single sample following the time at which the eye has adapted. There are [hopefully] no over- or under-exposed areas.
The dynamic range in HDR games is often used to simulate the entire process of eye adaptation. It's a function over time that intentionally creates over- or under-exposure some of the time.
> ask WHY games are the way they are, though.
To add to your point, the main reason for "bad HDR" in FPS games is for simulating eye adaptation. Screens don't have 1,000,000:1 constrast ratio and can't shine as bright as the sun (we wouldn't want them to). This means that games are forced to approximate this effect - inevitably resulting in shortcomings.
Furthermore, game development is a race against time. You have milliseconds to render the scene and apply tone mapping. It may very well be mathematically possible to create automated tone mapping that would make a cinematographer proud, but can you make an algorithm that completes in less than 1 millisecond? I doubt it.
To my point, there are mods on PC that replace the tone mapper (I think ReShade does this) and they absolutely destroy your framerate - however the results are absolutely gorgeous if you know what you're doing.