Yeah - without some sort of pre-processing or planning around the edge detection it’s essentially impossible to get ideal results. A specialized UV layout is one option but it’ll probably struggle with complex geo. A distance field or curvature texture is probably the way I’d go. Obviously if you’re going to use a texture you could just bake a normal map instead, but if the DF or curve texture works well then you’ve saved a channel since they can fit in a single grayscale channel, should work for any geometry, and wont need a unique UV index. Plus they can also be reused for other things like edge wear.
Even the ideal results will probably be inferior to baked normals, but this has the advantage of being able to control the look easily in real time which is nice, maybe save a bit of texture memory and add some extra utility.
The biggest flaw so imo is that because it’s interpolating across the whole edge, unless you have supporting edge loops, certain lighting conditions will look incorrect. Here, the shape is lit from above, but you can see the dark shading on the bottom 1/3 of the edge because by then the normal begins to point downward, even though the edge brightness should be consistent. (compared to true bevel + face weighted normal where edge lighting is consistent)
Extra edge loops would solve this, but then that begs the question of why not just model the bevel in if you have to add loops anyway.
Regardless, with some effort I think you can get good enough results, but I’m still not convinced it’s worth it.