Adopting a "grandparent" for your children is a recent, though certainly worthy, concept occurring in Western Society as an effort, whether conscious or not, to mitigate the impacts of familial fragmentation.
It was not very long ago in history that families of several generations and a broad expanse of inter-relationships living together was the norm rather than the exception. Generations of families were birthed and raised together in close proximity. In many parts of the world, this is still the case; they are the better for it, both emotionally and through social stability, no matter what their economic circumstances may be. Only the totally destructive disruption of famine, the social disorder from such evils as civil war or domination by external political forces can lessen that.
In the communities of Western Society it is now rare to find closely located extended families. Many families are far flung between countries, let alone states or merely cities. Many parents, whether they consciously recognize it or not, miss the familial support structures that were inherent to the close proximity that families and small communities previously occupied.
While conservative politicians often extort traditional family values, their concept of what such are is extremely limited at best. They seem to feel, or at least state, that the nuclear family, parents and children only, is both the norm for humankind and how things have always been. This is not so! Any examination of history or study of undisturbed indigenous populations would make that abundantly clear.
The ability to travel significant distances from the extended family is relatively recent; the habit of doing so only occurs in those of Western descent, and only since the early 1800s when the process of colonialism first became established. While some migrated in the hope of benefiting their children, finding a place where their children could blossom and succeed, many were given no choice at all by dominating "nobles" who would convict someone to 30 years of servitude on the far side of the planet for stealing a loaf of bread to feed their children.
Small communities is the natural way for humans to live. This normal structure, that existed for hundreds of thousands of years, has been deformed since the discovery of agricultural techniques has allowed the formation of much larger human communities, cities and nations. And in the last couple of hundred years, the fragmentation of extended families and communities.
Not only is it normal for young children to associate with elders two or more generations older, it is fundamentally beneficial to their mental and social development and well-being. Confinement to their immediate nuclear family and family friends and associates may well be the norm now, but the sociological ramifications of this is the steadily deteriorating society we live in.
The conceptual ability to feel for, and have some understanding of others, whether different from ourselves due to culture or age or not, is decidedly beneficial to the harmony of society. It is well known that young children have the greatest capacity for learning; given the chance they also have the greatest capacity for developing understanding of others and compassion. Parents that provide a social connection with elderly age groups for their children are not only expanding their immediate horizons, but providing them with a more natural developmental environment likely to gift them with the ability to not only tolerate but bloom in a Western Society that sadly is more likely to crush than nurture most children.
This certainly does not mean that adopting ANY elderly person as a "grandparent" will be beneficial to your child's development; not in the least! Throughout history only a few have successfully overcome the travails of life to reach an old age. Such people have perfectly legitimately been venerated for doing so, whether they have survived to such age due to skill, vitality or luck. A simple comparison of population demographics between technologically advanced societies and those still constrained to the realities of the past shows that that the elderly in Western Societies are numerically extensive due to the advances in medical technology rather than their own personal qualities.
The perception of many of Western Society's elderly is that they do not receive the respect and regard that the elderly did when they were young. They are correct, they do not. What many are unable to realize is the reason why. Where the elderly of the past reached their age due to their integral abilities, demonstrating the ongoing worthiness of the regard they were given, it is now impossible to tell whether a person of extensive years has reached such due to their inherent nature or simply because of modern medical technology.
An elderly person willing to be an adopted grandparent to your child is probably worthy of being so. Granting them the opportunity to try may prove rewarding to them, your children and yourself. Sadly, you will need to monitor and observe for some time in this day and age before you can be sure that you have chosen the right "grandparent". Providing such to your children, even if they still have all four natural grandparents about them, is a worthy and worthwhile gift; ensuring you have chosen correctly is a necessity.