I believe that this proposal has been made before and I think it is a good one. Even if there are still some things to be considered, first encounters or the start of the dialogue / a reaction are often dependent on the race. If I start a dialog as a [Human] and switch to [Drow] or [Tiefling] shortly after, I would find that strange if the overall context of the dialog flow is not coherent.
But if it's just the pure "skill checks" you mention, I totally agree with you. Beamdog did it quite well with the additional companions in the Enhanced Editions of the predecessors. (I don't know how it was with the vanilla version with the old companions). The MC could choose a dialog option where he called a companion by name and asked for his opinion. (Of course, Larian could then do the same for both companion opinion dialogs and skill checks accordingly). This should of course also apply to custom party members and would IMO increase the group cohesion considerably.
