The Fylingdales Stone 1
Image by fitzcoraldo

But surely this "who should see it" (this time "it" being all kinds of heritage ie Stonehenge, Silbury, Avebury...) is one of the major concerns of heritage conservation.

Yes it is in many different ways.

Members of this forum have secret places that only they (not me) know about (and some archaeologists).

The argument is never IF secrets should be kept, it is how best to keep them.