I went up to Holme-next-the-Sea on a cold winter's day. It seemed that the structure - whatever it was - belonged in its environment and to consider removing it to a "place of safety" would remove all its magic.
I have heard the arguments that the environment is "fragile" in that the peat beds may be eroded if too many people walk over them. Similarly, the many species of birds may be disturbed by crowds of sightseers. However, it is a very wide beach and it would seem a pity to remove it before more people have been able to see it.