Let's put on the yellow hat:
everyone from every culture would be needed to develop such a language...
Adults who learned it would be able to shape their mouths with the ability to speak all language requirements; It could be the test of flexibility in the ability to shape and move your mouth.
There would be no particular cultural stipulation to having an accent in this language. ;o)
Developing a new language could also allow the ability to pick which language to copy grammar from -
(I nominate the Hopi Language for structuring grammar and point of view.)
Perhaps the kids raised speaking this language would have no cultural bias!! Because there would be no particular culture connected to this language, being an independently constructed one...
OK, I'll stop there. Anyone want to wear one of the other Six Thinking Hats on this idea?
Do you know about Esperanto? It tries to do such a thing, with the additional stipulation of being easy to learn.
I have also imagined that perhaps a world-wide language would be cool. My choice was sign language, which is close to being internationally recognized by all deaf people world-wide. My choice came from it being a language that did not necessitate ANY mouth sounds. Then you could talk in your own language, and provide the hand signals as a translation of what you were saying in your own language.
Evidently the only reason sign language has not already been adopted as a "universal language" in this way, is because some cultures believe being deaf is a such serious shortcoming, that it is a social shaming.