True, but in that case, the motivation for having a copy in the first place gets a lot lower.

It isn't immortality. At most it's another version you create so your friends and family don't have to give you up. Which I can see being pretty motivating... but on the other hand, I can see the friends and family being totally unwilling to have a meaningful relationship with a second, slightly-diverged person after the first one died. And then the copy would be lonely. :-(