Wasn't it BK2000 with Ransom?
Depends on how you define wizard mode.
I still think earlier EM games had wizard modes, they just weren't called that.
Regardless, I feel a game's "wizard mode" should require a specific set of objectives be achieved through play, independent of what anyone else has done in the game. It can apply to newer or older games.
So comparing FH to BK2K,
FH requires a series of 6 modes be earned and played at the mirror followed by a final shot to the mirror starting the mode.
It is reset game to game and each player has to achieve the same set of goals.
With RANSOM, a player could be at the right place at the right time walking up to the game with RANSO lit, just needing an M. The effort is not necessarily equal and reaching it is not necessarily the result of achieving all of the objectives to receive the award.
Allowing the letters to carry over game to game was a dangling carrot to players to drop in some coin. Hey wow, I only need one letter!
If it were required to start from scratch each time, that would be different.