Just shoot everything in 20mm, because that is roughly equivalent to the human eye. Mark every photo with a different lens as distorted and potentially misleading. Journalistic integrity saved ;)
It depends on what you are doing with the eye. For example, when you are focusing on a single thing, like a person talking to you, then a picture with a 50 mm (135) lens generally looks sorta similar in terms of proportions and perceived perspective. But if you are taking in the scenery, a 50 mm lens would seem to be too narrow and you need a moderate wide angle to convey a similar feel. Similarly, intently focusing on a distant object will make a 50 mm seem to broad, and a 105 mm will seem more like it.
Note that professionally made panoramas are often made with more complicated and hand-tuned projections like Panini.
You really need to know the sensor size to adjust accordingly.
E.g. on a Canon 450D (crop factor 1.6) the equivalent of a 50mm full frame lens is a 30mm lens
Then again, it's also weird to try and guess what an average perspective would even be, as it's dependent on screen size and distance from face. I wonder how consistent the "arc-length" is between people and devices
For an intuitive way to visualize this: look at a few dolly zooms and think about what you are seeing in terms of geometry.
EDIT: Ah yes, I remembered correctly https://theonlinephotographer.typepad.com/the_online_photogr...
Absolutely. Focus length without sensor size (or film size) is a meaningless indicator for FOV.
But when it comes to a FOV being equivalent to the human eye, surely we should take display size into account as well. A photo made with a 500mm lens displayed at 4"x6" has exactly the same perspective as a photo taken from the same place with a 50m lens, displayed at 40"x60". In fact that small picture is basically the same as the large one cropped to the size of the small one.
It's a factor I never see mentioned. The usual explanation is that a "normal" lens gives more or less the same image when we look through the viewfinder as when we look directly, without the camera. But we don't look at photographs through a camera's viewfinder; we see them on our screens, on billboards, on prints.
And a single lens length does not solve a problem. What if you wait for people to leave a bus and capture at exact moment when they are out of the bus but haven't had time to disperse yet? What if you cut the bus out of the shot and extend it to the street.
Your idea is naive in the extreme in that it would solve anything.