I think the OP asks a very important question that has direct impact I believe on one of the other recurring posts about how to get the younger generation involved in stamps. The answer seems pretty obvious: unless you are able to get kids involved in organized philately leading to exhibiting, it is going to be a very tough go. And I imagine that those that exhibit, did so not initially, but after being in the hobby for a long time.
I would be interested in the OP's answer to his/her's own question, but here is my answer: nobody. In fact, the stamp collection has become as more of a joke within the family as in "don't stick that collection on me" if you precede me and "we have no interest whatsoever in the stamp collection." The former comment from my wife and the latter comments from my sons, approximately age 40. These are all highly educated people and I am not judging them when I list their responses. Just stating something we all have heard or if not heard, seen by facial expression as in "why would I want them?" Or "why do you collect that?"
As far as the stamps are concerned, this was a collection that was originally started by me when I was around 10, then I inherited
a part of my uncles/grandfathers collection ( mostly low value Central American stamps) then added by me subsequently when I got serious about collecting in the late 1980's/1990's. Ultimately this turned out to be a pretty good assemblage including several rarities. The boys interest does not extend even to asking about the rarities.
But the lack of interest is not confined to stamps; it extends to other phases of my collecting over the years including early coinage, currency, fossils, autographs. Again, I am not assigning blame or regret here, only reporting my own experience that I suspect mirrors many other readers of this post. The single area that seems to attract them is vintage sports, but again the interest is greater related to items related to events or people that occurred during their lifetime as opposed to items originating decades before they were born even if the item was signed by legendary stars.
Would I have loved to have a descendant take an interest in one of these fields to add to the collection as a family heirloom: sure. But I accept the fact that the younger generation of today's seems more interested in the here and now and the future as opposed to the past. Which is the way it should be, every generation deciding for itself what interests them. As a corrollary, however, and as it seems that the baby boomer generation has delved into collectibles much more than generations before or after it, and considering that this coincides with proportionally much greater levels of expendable income, I think this state of affairs says more about us than them.