But as Heather says, daily piano practice needs to be part of the basic expected routine for a child. No different than school homework, and perhaps more enjoyable. You can help or encourage, but threats are a lousy idea.
Peter, the biggest reason why threats are a poor idea is that they don't work.
By the way, I still believe in consequences.
If a child is pushed to play from the beginning and does not like playing there is a huge chance it is never going to work. I do not remember being forced to do anything I hated, as child, where I did not stop as soon as I could, and I don't recall saying later: "Gee, I wish I had not stopped."
But there are a lot of kids who WANT lessons and do well at the beginning then suddenly want to quit the first month or week everything doesn't go fantastically well. What do we teach by letting kids always decide to quit anything the moment it gets hard? What do we accomplish ourselves by doing the same thing?
So I think even a child has some responsibility to continue for a reasonable period. Then later that child should also have the right to renegotiate, at the end of the year, at the end of a couple years. Something like that.
Until an agreed upon period is up I think the proper answer to quitting is simply: "No. That's not what we agreed on."