What resolution is needed for 360 video?

I got my basic 360 video viewer working and was not pleased with the resolution.   I've realized that people are really serious that they need very high res.   I was skeptical of these claims because I am not that impressed with 4K TVs relative to 2K TVs unless they are huge.   So what minimum res do we need?    Let's say I have the following 1080p TV (we'll call that 2K to conform to the 4K terminology-- 2K horizontal pixels):

Image from https://wallpaperscraft.com

If we wanted to tile the wall horizontally with that TV we would need 3-4 of them.   For a 360 surround we would need 12-20.   Let's call it 10 because we are after approximate minimum res.  So that's 20K pixels.   To get up to "good" surround video 20K pixels horizontally.   4K is much more like NTSC.   As we know, in some circumstances that is good enough.

Facebook engineers have a nice talk on some of the engineering issues these large numbers imply. 

Edit: Robert Menzel pointed out on Twitter that the same logic is why 8K does suffice for current HMDs.