Why does Mandarin differentiate 发[發/髮] fa1/fa4 when most topolects don't?
We might never know the real reason. All those rime books indicate that 發 (out) and 髮 (hair) are always the same pronunciation, and both are entering tone (入聲). This means there is a terminal -t in pronunciation on 發 and 髮. We know that when -t was lost in Mandarin and the tones became unstable. In Chinese phonology it is named 派入三聲. The entering tone (入聲) was gone and all characters in entering tone go to the rest three tones, namely the flat tone (平聲), the rising tone (上聲) and the leaving tone (去聲). In this way, it is possible that 發 and 髮 develops different tones in Mandarin.