Everything in the world has a U-shaped value curve. Most valuable when it is new, at some point it loses value, may even become worthless. Down the track, it will become priceless and irreplaceable. Note 'value' here isn't strictly monetary, it can be cultural as well.
Dropping buildings in the midst of the U never gives things the chance to recover and move past fashion. Most buildings discarded are due to the design being old and out of date. But old buildings in a city plant the cities history in time and allow it to tell a story. Remember that 'Gothic' cathedrals were so named because the term was in regular use as a description of something vulgar. The Notre Dame in Paris was at one stage due for demolition until the story of Quasimodo re-inspired the public to keep it - the restoration is still ongoing.
Buildings can be re-purposed and still keep their charm. The mistake is in discarding things just because they are old.
It's very true that not all old things are worth keeping, but the benefit of the doubt must go to the building until the current fashion has moved into the past.
Also, in the case of Berlin, a lot of damaged structures have been reinforced and kept standing as they were at the end of the war. It reminds the city of what can happen if continual efforts towards peace are not made. These scars on the landscape are a constant reminder of the cities turbulent past, and help develop a sense of the story of the city while walking around.
Buildings are the ultimate encapsulator of society - it's where we live, die, make decisions and create history. As such they have a special importance in being kept to tell that story to newcomers.