I always though the reason I found this more enraging than the beheadings was because human life, at risk of sounding callous, is 'expendable' in that there are billions of us, with new humans being born every second, but these artifacts are literally irreplacable.
I had a conversation with my SO with regards to the destruction without mentioning my view on why it affects us so much more and she pretty much came to the same conclusion.
And from a utilitarian point of view it teaches us that there are more points of view than just Islam. It might save a few lives in the future knowing that one group doesn't hold the monopoly on the truth.
Think this through a bit more because your explanation is lacking. Humans make objects every day to replace things. There are more expandable objects than there are expandable human beings.
Nimrod was suffering to exposure to the deserts prior to this. Now it's gone. Much like how plenty of things throughout human history that holds great value goes away.
Things we don't even know of or comprehend of value also goes away.
You thinking the destruction affects you so much is purely because of selfish ego.
I had a conversation with my SO with regards to the destruction without mentioning my view on why it affects us so much more and she pretty much came to the same conclusion.