I'm really interested in the why. Most people don't seem to care. My in-laws have CFLs in their living room that just feel horrible to me, but they're none the wiser. I'm very curious as to what it is in the light spectrum that seems to matter to some (small) class of people, myself, and it sounds like you, included.
The word for "fire-like" light, used in my original comment, is "black-body radiation". Stars, fire and incandescent bulbs put out a similarly shaped spectrum.
A few years ago there were scientists working on a black-body (i.e. incandescent) light bulb that reflected infrared emission back to heat the filament and re-emit as visible light making for a theoretically efficient incandescent bulb. I check every year or so to see if the research has been commercialized, but have always been disappointed:
https://www.dezeen.com/2016/01/13/mit-energy-efficient-incan...
Edit: Another point on the blueness of LEDs is that they seem to amplify macular degeneration, which has made my grandmother mostly blind, and I know based on gene sequencing that I have a more than 50% chance of developing. While most of my rejection of LEDs is based on them not looking nice to me, I am also worried about hurrying the onset of blindness in old age for persons like myself who carry the genes for macular degeneration:
https://edition.cnn.com/2019/05/16/health/blue-light-led-hea...
Personally, flickering makes me ill. I am used enough to 120Hz to survive it, but any other frequency is bad. Also, the 6400K LEDs look way too blue, much bluer than the Sun. That may be because I have a relatively rare kind of color blindness.
regarding 6400k - even assuming the sun's spectrum matched the black body spectrum of its surface temperature, its surface temperature is closer to 5770k. but even taking that into account, its spectrum doesn't quite match 5770k in space - and the atmosphere changes it even further. https://en.wikipedia.org/wiki/File:Solar_spectrum_en.svg
I really don't know how much of that change us humans can perceive, but my thinking is that 5000k is probably closer to the center, at least. it might be more of a saturated color, though, since the spectrum is more pointed vs the very flat but spikey spectrum in that plot.
Flame, not entirely; embers, yes.
My first suspicion would be the spectrum of light emitted, which is mostly reflected in the CRI [1].
CFLs in particular "cheat" by having a couple really strong peaks of very specific wavelengths that to your eyes (or reflecting off a white surface) look like the right color, but when reflecting off anything they have reproduce colors inaccurately -- it's beyond my ability to explain this in detail, but you can see this in some spectrum charts [2].
LEDs vary greatly in this respect, so if you're concerned, you should really be paying close attention to the CRI (and note, as CRI goes up, so does cost).
[1] https://en.wikipedia.org/wiki/Color_rendering_index
[2] https://www.ledsmaster.com/color-rendering-index-cri-versus-...
I'm a bit miffed it seems so hard to find lights that don't have this problem, though. maybe we can improve it by getting the word out that these cheap little diffraction devices can give you a pretty good approximate reading of the smoothness of the spectrum of a light source. Hmm, I just realized I have yet to take this to home depot...
I'm really curious about those MIT incandescent bulbs. If they worked well and haven't been brought to market, it's possible that contacting the people involved in creating them could have good results in making them happen. Perhaps they could be convinced to prioritize it if a case can be made that it can have a significant positive impact on the world?
Another thing I hate is LEDs with such a sharp point source them make speckle patterns like a laser.
But I did find some good LEDs and I'm using them now, them seem as good as the CFLs they replaced. Had to return a bunch of bad ones though.
I've found that high CRI warm white (2700K) bulbs are the way to go for me.
I have these at home, and I like them a lot: https://www.lowes.com/pd/GE-Relax-60-Watt-EQ-A19-Soft-White-... . (I bought them at Home Depot, but it looks like they no longer sell them.)
Phones are pretty bad too. Check out the Nexus 5x vs Pixel 3: https://drive.google.com/drive/folders/1f7-ChF4zFiisFdmEZVEz...
I found that Phillips non dimmable bulbs are the cheap and don't flicker.
I'm currently experimenting with 'emulating outdoors' in my office environment for health and productivity, and so far I've started with an 8,000 lux fanless corn LED (bought off Amazon) hanging from the wall and it's brilliant. I immediately feel 'happier' when I turn it on in the morning, every single time, but after a while, I agree, something feels off. I feel 'cold', temperature-wise.
I have read (no source for now, just from memory) that having bright white light indoors (e.g. fluorescent) without the presence of other light spectrum (including possibly natural UV) can actually increase cortisol.
So I think that more than just visible light is needed to complete the picture. Careful, low enough levels of UV and infrared that doesn't point directly at you but more 'above' you like the sun itself, may be the optimum to get some benefits but not cause dangerous skin or eye problems.
The yellower are similar to a mid summer day and I can cope with them, but there's always this feeling of something being off. I guess it's connected to us humans being used to non-sun light being (similar to) a fire - mainly consisting of yellow/orange tones.
Also, I don't exactly remember from where I read this, but when a (town) changed the street lights to LED's, a lot of people started having sleep problems, and it supposedly was connected to the blue light emmiting properties of (lower quality?) LEDs.