That's a variation called "full Cali". Nothing wrong with it, but its not the way its played competitively in leagues here as the players feel it gives the Cali player too much leverage. Its also apparently not the way they do it where the OP lives.
I think the moral to this story is that doubles is a fun format that you can bake in a lot of different flavors. None of them particularly wrong.
hrm, read it wrong then. I think it definitely is a disadvantage to the person then, and they should never be made to pay twice since they don't even get the same amount of throws as other teams. There are many botched upshots or putts that I would much rather have a partner to back me up on, than one good ace. I personally would not even use my extra shot off the tee most of the time. I would save it for a putt or approach (if I could do this)