Even if those six were the actual primary and secondary colours, it wouldn’t be necessary to have a primary word for each. You can refer them by hue, or by referring to some object.
But you don’t - that’s why languages lacking these words run into issues as described in the article.
The wheel that you’re implying by those six colours is mostly an artistic “distortion” of the 18th century.
But isn’t there a good reason it was distorted that way?
Of course some colours take up much more or much less of the visible colour spectrum, but that doesn’t mean they have more significance to us.
Like red taking up over five times more of the colour spectrum than yellow doesn’t mean that all these reds need to be named. Most red tones are hardly distinguishable to most people. Yellow and red on the other hand can be distinguished with ease.
You won’t run into the issue of differently coloured traffic lights in english countries; because while the traffic lights might use slightly different shades of green, they don’t use drastically different colours - because we properly named them.
Why is it impossible? The simplest possible way would be to hold new elections in Gaza for which Hamas do not run.
It would probably lead to a group identical to Hamas being elected, but it would be neither Israel nor Hamas.
What may be impossible is a government that’s aligned with western governments, but that’s not what is being asked for.