The soul is definitely alive.
According to the Book of Luke, concerning the story of Lazarus and the rich man, one soul was in hell being tormented and the other soul was in Paradise. If we go by this story, then the souls of those who denied God/unsaved are indeed in Hell
I've always thought that people just go off into eternal sleep when they die, awaiting the resurrection upon Christ's return. And at that time when Christ returned, those in Christ would go to paradise.
But if it is really so that when a child of God dies, their soul immediately transitions to paradise, then yes I would agree that under such circumstances, we should not delay the process.
But then I've heard stories about people waking up after years of being in a coma... so God was not ready to call that person home as yet...
But I wouldn't want to take this decision for myself or a loved one. That's a tough one, so hopefully God will make that decision for me, if God forbid, I was ever asked to choose.