Is the Nostratic Theory plausible?
The idea that the majority of languages are all connected doesn't seem so crazy, it could be possible that the coming of a language is a rare occurrence.
As far as I know it seems writing only occured separately in China and Egypt, Egyptian hieroglyphics being the precursor to the most alphabets used today, although I'm probably wrong.
Why isn't more research being done on the Nostratic theory?
Writing is an extremely sophisticated concept, it's no surprise it has only emerged a handful of times.
Speech much less so. Lots of animals have some means of speech that they almost instinctively know how to communicate with. Even man has this despite having a much more sophisticated means of speech, since if you start yelling at someone in any language they'll know what's up.
writing originates from mesopotamia and it was the cuneiform alphabet, the first known form of writing. if all alphabets originate from it or several alphabets were developed later separately from cufic its possile but writting occured first in mesopotamia.
It's rightly considered a fringe theory because it's outside the boundaries of historical linguistics. You can't reconstruct anything as far back as Nostratic would be with the comparative method.
Writing also developed independently in Mesoamerica.
You're working under some very basic misconceptions. The introduction of writing doesn't cause language shifts, and writing came about thousands of years after the proposed origin date for Nostratic.
Writing was developed independently in China, Egypt, Mesopotamia, the Indus Valley and Mesoamerica.
It's true that all modern writing styles ultimately descend from either the Egyptian or the Chinese one. But the mesopotamian one was very influential too in the past.
To awnser your question, that wasn't related with writing, I think this anon >>571994 gives the more sensible awnser. We just can't obtain enough information to research this subject.