I believe the death of a hero is appreciated in today's world. I believe the world is full of heroes and generally they get the recognition they deserve both while they are alive and after their passing. People who pass in attempts to be a hero to someone also get recognition, generally locally, from the people they impacted.
There aren't heroes like the ones of the past, romantacized and loved by all, but there are still heroes. For example, look at how well firemen are treated by the citizens. They are like the ultimate heroes. And then you have military service people. They actually get rounds of applause at air ports.
The definition of what a hero is needs to be addressed first. Those men and women who fight and die in the name of their nation's government could be considered heros. The men and women who fight and die in the name of eradicating their nations government could be considered heros. What does society consider heros? Celebrities. When a celebrity dies, even if he/she dies from something completely preventable like a drug overdose, they are heralded. A father may be the hero to a son, and upon his death that appreciation of a hero will be witnessed. But no public heros exist anymore. They aren't press worthy.
Yes, I believe the death of a hero is appreciated in today's world. Although I feel it some aspects a hero does not meet the same criteria as what it once did as far as meaning to people, I still feel people appreciate them. Perfect example is a fallen soldier in the war or Nelson Mandela. Two very different heroes in there own respects, but both were equally appreciated among those who believed in them and saw them as something special.
An example of a modern day hero who was celebrated for his contributions to our world was Nelson Mandela. People world wide acknowledged his passing and presidents and worlds leaders from all across the globe were at his memorial. His death was very big news in a world obsessed with always trying to find the next best news.