One could more easily make the leap from Egyptian Hieroglyphs, being originally designed for an Afro-Asiatic language with consonantal roots, to an abjad than Sumerian cuneiform, which is a complicated and irregular logosyllabary; I have taught myself some Sumerian and cuneiform, and it can agonizingly complicated and irregular, if very rewarding. While Egyptian hieroglyphs are complicated, they do fit Egyptian quite well, while Akkadian is a very poor fit for cuneiform.

Thus, once a simple phonemic system arrived, it became much more practical to adopt the far easier new system. Chinese characters survived because China has been very enduring and culturally dominant in East Asia, while there had never been a comparably enduring power in the Near East.