<BuilderQ: In the beginning of the gaem what you say is true, but I have just found another game where the double move would provide me with a significantly stronger position.

Ibelieve the benefit for black only really begins in the mid to later parts of the game, once a few pieces have been cleared. One of the problems black has is the time it takes to get their pieces to the queening line ... this change would reduce that time by one move and, where games are sometimes decided by only one or two tempi, this is possibly a subtle change which can partly (fully?) redress the inequalities.

If it were to be considered further I would suggest that any black pawn on the rear two rows might be able to move two ranks if possible which would give:
rank one -> rank three
rank two -> rank four
AND rank one -> rank two -> rank four (2 moves).

White could then take using enpassant (sp?) in the usual way for 2->4 or also in a corresponding manner for the 1->3 double move.

What do others think?