And jazz and pop and rock and.... It is a universal language that allows musicians from many backgrounds to come together and play a tune together. Jazz is the most obvious example--where musicians often sightread a tune together. (Although, to be fair, a substantial part of jazz notation is chord symbols, which are not (directly) a part of traditional notation.)
lead sheets are solving a whole different problem and almost ALWAYS have the melody in traditional notation in addition to the chords. some lead sheets assume you already know the melody and can transpose to whatever key is relevant.... but still a lead sheet is there to give you hooks in order to aide improvisation.
jazz musicians have not "split off", they have added some chord notation above the traditional stuff.