Is this a joke? Of course a 6" screen doesn't produce as much as a ball of nuclear fire
But that ball of fire isn't 12 inches from your face at midnight. And, the majority of blue light filter use is targeting sleep quality. A good portion of this comes down to cumulative exposure time. The best solution is to just not look at screens after a certain hour, but no one wants to do that.
Blue light suppresses the release of endogenous melatonin. To get an idea of how much it suppresses, it, take a look at the image below. In this image participants were exposed to no light, or a 2 lux light at 460nm (blue line) or 560nm (green line) for 1.5h. source
As for the mental stimulation part, that's going to vary a lot more from person to person and how engaging the content is, but you're right that being mentally stimulated in the wrong ways can keep you awake too.
Blue light has a documented effect on our circadian rhythm and melatonin production. It's been studied quite a bit. I'm sure mental overstimulation is a component, but it absolutely is not the whole story.
In Western society, there is a big focus on silver bullet solutions because people don't want to address issues in a holistic way. Thus, you have blue light filters instead of turning the screen off.
No. Typically the sun is brighter. Also if your device is set to 9300K color temperature then it has more blue then normal. The sun is about 6500K and all display devices should be set to 6500K or SRGB where possible for best color rendering. Pros actually have a color calibration device to do even better.
Color perception and maybe eye strain also depends on surroundings. That is why having a neutral background behind a display that has a similar illumination level is recommended.