You can very closely simulate a reflective display using an emissive display and ambient light sensors. That's what Google's Nest Hub Max does, and it very often looks like a framed photo (i.e. reflective).
It's not like photons coming from an LED in a panel are more damaging than those same photons coming from an LED in the ceiling, that then reflects off of e-ink.
Outdoors, the problem is that transmissive displays are not bright enough to beat sunlight. That's where e-ink makes more sense, and where I think there could be a real health benefit (outdoor sunlight exposure, ability to focus at long distances).
My angle is that we don't need complicated e-ink + LCD displays. Just make LCD less straining (reduce glare, automatically limit brightness).
But I also don't know why they aren't more explored. Grayscale ones would make for excellent e-readers. And you can always make the bottom layer both reflective and emissive, making the thing work well both outside and in a dark room.
My guess is that LCD just standardized on a level of quality, and you won't get anybody producing anything different.
At the time quite a few other e-paper screen technologies popped up which had much faster response times than E Ink's electrophoresis displays (Liquavista, Mirasol) and some even had (in theory) better potential to make subpixel-free color screens possible. Unfortunately none of them could quite match the contrast (and perhaps price?) of E Ink's monochromatic screens. Which was fatal, as e-readers were the main application of those screens, and those really only require a black-and-white image. So the other technologies were abandoned.