E.g. Newegg video suggests installing CPU/cooler on MB outside of case, while other videos install after MB is seated.
This is a good point. Some cases actually have a large cutout on the motherboard tray so that you can do the entire cooler installation with the motherboard already mounted, including installation of the back plate.
Personally, I prefer Newegg's method, to do the entire cooler installation outside of the case. Air coolers can be tricky (and obscenity-inducing) to install sometimes, and it's made worse by having to deal with the hassle of installation in the case, where you can't simply maneuver/rotate the motherboard as needed. By doing the installation outside the case, you also get a closer, well-lit view of your thermal paste application and the evenness of the tension/pressure of the mount at all angles.
It might make a couple of motherboard screws a pain in the arse when you have to mount the motherboard with a giant heat sink in the way, but it's manageable. I always take my time installing coolers, and even now I still feel like I could've done a better job after I finish installing it.