Short answer, from my view, is that if we've screwed up lighting enough that we need supplements, the easier option is to fix lighting.
The savings on my utility bill were immediate and more significant than I expected, and the bulbs themselves were not cheap. So I'm a bit hesitant to switch back.
I've already taken melatonin supplements on and off for years with positive results: I've had sleep issues since I was a kid, definitely before I was in front of LED-lit screens all the time, and well before home LED lighting was a thing.
I may be suffering from some sort of sunk-cost fallacy, but especially given that I've always had (probably non-light-related) sleep issues, it feels "simpler" to just leave my lighting as is, and take some melatonin a few hours before bed. Obviously I'd prefer LED lighting that has better spectrum emissions, but as you note elsewhere, that product would be significantly more expensive. I do agree with you that it seems perverse to break ourselves with our technology and rely on supplements to fix it, but I think wholesale going back to incandescent lighting just isn't going to fly from an energy policy perspective. And I don't think burning fossil fuels in our home (kerosene lanterns) is a great idea; that's just trading one health problem for another.
I think at this point our realistic choices are: a) finding a way to make efficient, cheap "white" LEDs that don't blast out blue light, or b) some new yet-to-be-invented technology that has similar power consumption as LEDs, but healthier emission spectra. I just don't see incandescent lighting (or kerosene lanterns) as serious, realistic contenders for the future.
Edit: it seems OLED is actually quite a bit better when it comes to blue light emissions? (https://www.oledworks.com/news/blog/the-hazards-of-blue-ligh...) I wonder what is holding OLED back from consumer lighting. Perhaps cost?
Lots of good discussion and links to studies about efficacy here: https://gwern.net/melatonin tl;dr - yes it works and is much easier/cheaper than other things