That is the point I am making, many of us have items in our houses that are of deep sentimental value to us and attached to family stories, but stories are best put down in written form and whatever our children may promise us in life, they can do what they like with it after we are gone and we will know nothing about it.
However much we may want to we cannot make our descendents keep things that are precious to us that they have no use for, nowhere to put and will be, as far as they are concerned, millstones around their necks if any attempt is made through wills and the like to force them to keep them.
If you have items of value that that your children may not realise are such, tell them and advise them to get specialist dealers in to value them and recommend how they should be disposed of.
I am fortunate, most of the family have an interest in antiques, well, old stuff anyway, and trade regularly on ebay, so I am pretty sure that DD will make sure that all we possess is kept, sold, where possible; freegled or sent to a charity shop and very little will be tipped.
Anyway, whatever is done with our posessions we have little or no control over what happens once we are dead, and won't know anyway, so why worry?