I agree with the sentiment, however in some ways it should be something that is permitted to move.
The UK has been very stable for a long time, however they are profiting indirectly from the museums, since it s a driver of tourism.
Should the UK become less stable, we should have a hard look at ensuring the continuity of the collection. As others have mentioned, a lot of these things would have been destroyed or forgotten had the British not decided it was important to keep it - and as time goes on, those things become even more irreplaceable.
If the UK became less stable, maybe someone like Germany could take custody and seize the collection, for UK's own good?