The worth of family values depends upon families, I think.
I hope that when (or if) I am a great grandparent I can remember that the important grandparents are my children, not me. So, yes, if I cannot help but interfere; irritate; demand attention and so on, I rather hope my children will put me in a cupboard, so that I cannot spoil their joy in being grandparents.
As to benefits from great grandparents, does that not also depend upon the relationship between them and their great grandchildren?
As to relationships, I have to say that yes, I do have a better relationship with my children than I have ever had with my mother. My mother has always been self-centred, and that included when I was a small child. She did not even look after me - that was left to my grandmother.
So I feel the same as Jan. My time with my grandchildren is precious, limited already, and is destined to be limited even more since they are growing up so quickly. I will not willingly sacrifice my time with them for anything. But I do, and have to, mix the generations, simply because although our family values may be wanting, they do include avoiding giving unnecessary hurt to its members. My mother sees the grandchildren about half as often as I do, and spends a great deal of time in between complaining that she doesn't see them often enough, and "isn't it a pity that they live so far away".
Perhaps judgements should depend upon knowledge of circumstances?