The main reason for the convention is that hydrogen's valency is one ALWAYS. And sulfide is a reference to the -2 oxidation state of sulphur. So, hydrogen sulphide can mean only one thing, because there is only one SULPHIDE of HYDROGEN.
Take in contrast the case of the oxides of nitrogen. NO, NO2, N2O, N2O4, N2O5. Here there is a need to specify the valency of each element explicitly in the name. Nitric, nitrous, dinitrogen pentaoxide, etc