I don't think soldiers or accident victims have the same emotional value to other people as certain celebrity deaths, and not just because of psychology or whatever, but for legitimate reasons. The sadness of a death generally doesn't come from the death itself, or the fact that they are people, or the fact that they didn't deserve to die; those can all make it worse, but they're not the root cause. What really affects people is the sense of loss. Anyone who respected or followed a public figure will have good reason to feel like they've lost something when that person dies, and this is a type of bond that soldiers and accident victims generally don't have with the public. A soldier's death is sad to the people they knew and loved, but there's no emotional connection to strangers.
I wouldn't say I was familiar with Amy's music or personality, but from what I've heard, she had a lot of talent and was creating some solid and significant work in a musical genre that had been all but forgotten by popular culture. To people who appreciated her music, her death marks the end of her innovation - the talent is gone, and there can't be any more new songs or performances, just what has been recorded already. So I think a lot of people see her death as a signal of the world losing a rare talent, one which can't be brought back. There's something deeper here than just "oh, it's a celebrity".
