This makes sense. But it is probably of little practical value; in the initial position white will have wide choice of nearly equivalent opening moves, end when you block one of those, he will simply play another without significantly suffering from it.
Duck chess: suggestion

Black can also reserve a square for themselves. E.g. if you want to push e pawn, you can put duck on e6, that guarantees that you can move it.
True, but also there it is not very likely that you would need that move, (which depends on white's first move). And even if you did the reserved move will probably not be very much better than an alternative. So it will have little impact. It will have some, but not nearly enough to neutralize the first-move advantage.
Would it be more fair if Blacks would put the duck first? It looks more logical to me: Every time you move there is a duck somewhere except the Whites' first move. Whites have advantage anyway in chess, why give them additional advantage? I think the rules should be changed, so Blacks put duck (without making move), then Whites make their move and move duck as usual.