According to this answer to a question about the early use of green monitors they had a severe disadvantage in that you had to choose between 'too dim' and 'rapid burn-in' whereas amber could display decent brightness without burn-in.
It's be rather careful in accepting the conclusions made there. I can show you several green screens that have been used for more than a decade without burning in. There is no real difference between either coating. Of course if one pulls up the volume to excessive bright, all screens will burn in.
If amber was that much better, why did anyone use green?
Maybe because green is way better? The human eye has its highest sensitivity near to the red side of green (*1,2) thus a (somewhat) yellowish green is about the best colour. At the same time the sensitivity for brightness (*3) is to the blue side of green. In turn, orange/yellowish colours are as good for fine colour separation, but less sensitive to differences in brightness. So when it is about a monochrome screen, green outclasses amber.
Bottom line: The highest over all sensitivity, as in ability to separate levels of brightness and detect colour, lays right around green.
Was there any other reason to prefer green over amber?
Does it need any other than that?
The P Numbers you cite are not really related to any date of 'discovery'. They where an attempt of the RMA together with the US Army to standardize the components used for CRTs in the mid 1940s. The original order of the first few, declared at once, was in time of their persistence. That means how long the image would stay without being refreshed.
For example P1 and P2 have a quite close colour (P1 covers P2), but P1 continues to emit considerably longer than P2, so P1 is the classic green for early radar (and oscilloscopes used for low periodical signals), while P2 is used only for oscilloscopes.
Further, P1 is most definitely not the one used for green computer CRTs. It got a decay time (*4) of about 100ms. Any refresh frequency past like 15 Hz or so would result in an extreme blurred screen. Its low writing speed is another no-go (*5).
For most green screens in the 1970s and later, P31 was used. It is not only about three times brighter than P1 (at the same energy *6), but also has only about 30ms decay time, which goes well to display 'fast' content at 50-60 Hz without starting to flicker.
*1 - The colour sensitivity has already been discussed.
*2 - I guess that's a result of us having evolved in a green coloured environment ... well, at least back when we still climbed trees :)
*3 - The majority of information our eyes deliver aren't about colour, but black & white.
*4 - Decay time is the time a once initiated spot needs to go from 100% of its (specific) brightness down to 0.1% which is considered off. It is usually in reverse relation to absolute brightness - as the brighter a given coating is when ignited (at a given energy, like 10kV), the faster it decays - as a rough guideline.
*5 - Having said that, P1 has been used for some screens until the mid 1970s. Some may remember screens (mostly vector in addition) that had an incredible blur when scrolling. It felt like an age until the old picture vanished under the new.
*6 - Less energy for a given/intended brightness also means less radiation (X-Rays) toward the user.