"...the only way I can see to have NO first-turn advantage is if the first player has literally nothing useful to do with his turn. No possible piece development, no moving forward to claim extra territory, no starting to launch an attack or race for a promotion..."
Well if White could do nothing useful with their first move, the advantage would pass toi Black rather than be eliminated altogether. Such a rule cannot be applied to the FIDE array anyway, as there are no sideways moves until some pieces have moved anyway. You could insist that White move a Knight on the first move and the corresponding Rook on the second, but that would really give Black the advantage.
I'm not sure what effect a rule that White had to start with a one-step Pawn move would have. In the long term it would hand Black the tempo advantage, but it would still give White the chance to open up their diagonals earlier than not having the first move would - and give White some advantage of initiative.
Well if White could do nothing useful with their first move, the advantage would pass toi Black rather than be eliminated altogether. Such a rule cannot be applied to the FIDE array anyway, as there are no sideways moves until some pieces have moved anyway. You could insist that White move a Knight on the first move and the corresponding Rook on the second, but that would really give Black the advantage.
I'm not sure what effect a rule that White had to start with a one-step Pawn move would have. In the long term it would hand Black the tempo advantage, but it would still give White the chance to open up their diagonals earlier than not having the first move would - and give White some advantage of initiative.