I don't use a press either, but I am sure the advantage would be the consistency a guy can get by using one of them. I am not aware that the tensions of the individual reeds can be varied using a press, however. Perhaps there is a way to do that,...not sure.
I do like the flexibility of stretching the reeds individually,...and that gives a guy a lot of room for experimentation in call building, but that can have its good points and its bad points. When you add individual reed stretching to the call-building mix, you just add another variably into the almost endless combinations of factors,....reed layering, reed thicknesses, spacing, cuts, and tensions,....to consider in building calls.