My analysis of Gertrude Stein strongest idea and greatest value:
She realised by using stream-of-consciousness writing that language could be reassembled freely, and that concepts were arbitrarily created. She had an intuitive grasp of the boundary-lessness of the Infinite, where associations can be made between any things at all. However, she wrote copious amounts of literature in that same style, which means she couldn't make the leap to realise that ordinary conceptual associations show the same boundary-lessness. This means Stein was more attached to appearing to be original and having an interesting reputation, rather than truth.
It has to be said that her strongest idea was weaker than its expression by the likes of Billy Connelly, or David Byrne, but on the plus side, she can claim originality as she wasn't borrowing from other writers. She was influenced strongly by artists, and others in her 'salon' culture. She had fairly strong visuo-spatial thinking ("A writer should write with his eyes"). She also stands out because she was publicly lesbian, when it was by no means politically correct. This does indicate that she valued individuality and living as Nature determined. Nevertheless, she wasn't prepared to give her all to Nature... So, although she may seem to have set an example for the emancipation of women, she only reinforced their egotism by cramping her truthfulness.
Amendment: I take back that Stein's strongest idea was her originality in writing stacks of stream-of-consciousness stuff. The basic idea of the freedom of language was already well-known in the eighteenth century. Going to the trouble of demonstrating it, is little more than a celebrity stunt.
Also, women prior to her era were prolific letter- and journal-writers, and much practised in effusive streams of emotional writing. Probably her greatest accomplishment was turning women's letter-writing into something more intellectual. That's not disparaging it in any way; I think it may have helped slightly to turn some people's attention to the nature of consciousness. Not a huge contribution, but something.