[Quoth]

There are now very good LCD screens, my 23″ 4K monitor is just like using paper. Superior to any of my eink ereaders.

However I've not yet seen such a quality on a phone or tablet. We now have an Apple store in the local Mall. I don't see that quality there. It's nearly non-existent on TV screens, though better ones are not too shiny.

There are two separate main issues, apart from massive charge run time:
1) Is the OLED or LCD screen actually harmful to your eyes?
2) Is it more relaxing using only reflected ambient light, eink.

1) If the brightness is adjusted properly there is no harm to eyes, not even from blue light. It's possible that it's activity on a device rather than blue light that affects sleep according to recent studies.

2) A 220 dpi to 300 dpi resolution and ambient light and really only being able to use it to read (games & video & Internet awkward even if supported) is as relaxing as a paper book. Using a front light, even if amber tinted seems to reduce that advantage as does "dark mode".

Shiny screens cause headaches. Most eink panels are matte finish, most phones & tablets are shiny.

A big issue with tablets and phones is shiny screens. I've not bought a laptop, monitor or even CRT in nearly 30 years that had a shiny screen. Matte finish seems rare on phones and tablets. The problem is that any reflection is at a different distance to the text. You'll unconciously refocus on that if the screen moves or the reflected object moves. That will give an eyestrain headache. That's been known for decades and thus there is advice about not siting computer screens where there will be moving reflections.

Many cheap laptops and screens still are very shiny because it's far cheaper and the demo images in the show room look better.