Opening province is pretty nice
Opening Province is pretty terrible! If you could buy a $3 Province on your opening only, it would be the wrong move most of the time. A Copper that's worth a lot of points is a little better, but still not worth it a lot of the time.
The factor making it slightly different is that it's an option that if you don't take, your opponent can deny to you. I would take a Copper Buy to start the game for a permanent 6 point advantage on quite a number of boards, especially if the alternative is playing down six points.
Then again, boards with Castles and Keep have a lot more points to play with in the first place, so...