When have you heard of a poor person saving for their grandchildren?
It probably used to be done a lot, indeed is still being done in some countries.
My mum's mum who married a gent from another country and went there, when she came back to England and she died seven years later, it then took nearly thirty years to get her remaining assets out of that country for personal reasons I'll not go into.
Up to that point we lived in a house with a flat roof with a crack in it (when it rained dad would put a bucket in the middle of "the" bedroom and occasionally borrow a ladder to put tar up there), and after that because Mum could put a deposit down, we moved to a better one.
(To my delight while we were at that house, the Vickers Viscounts and Bristol Britannias kept flying low over us, and the wonderful Vickers Vanguards would come in over my junior school.)
Mum's mum hadn't had a job that I have heard of (the girls were still young) and mum's dad was a clerk.
My own dad was a shoemender turned clerk and my mum only got odd jobs till we were quite big, and even then mostly not very grand ones.
My brother now says he thought at the time we weren't eating well. I thought we only had just enough and I scrape my plate to this day. Looking back, I marvel how few changes of clothes we had. We had no fridge and no phone till I was 11 and no car till I was 21.
Mum bought the new house by taking threepences to the corner box and used to come back swearing about "Mr Crawley" (the conveyancer)!