My first point is preservation where is some random person/country going to keep a fragile ancient artifacts without a museum? If it is so treasured why leave it to rot in a closet, freezer, pocket etc. After years the artifacts must be fragile. Remember this is not a toy car buried in the dirt from when you were five which you can keep in your pocket this is piece of history and discovery.
Relating to my first point of history and discovery, what use is it to rot? What are the benefits? In a museum scientists can reasearch on this to determine how old it is with the help of carbon dating and they could see the impact on history. Like the Sphinx's nose. If you found it what use is it to you? On the other hand the museum can find out how it fell off and to improve architecture today.
if it's in a museum people around the world can learn about many magnificent things to improve their future. This will benefit you too and you'll think to yourself "I'm glad i donated this to the museum."