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Quote - "Given the amount of children they had, it is strange that Edward and Elizabeth did not have many great-grandchildren."
Was it really all that strange? It seems to me that this happened to quite a few dynasties.
Henry IV had a sturdy brood of four sons and two daughters, but by 1448 was down to a single legitimate grandchild, Henry VI. Henry VII and Elizabeth of York had two sons and two daughters who survived infancy, but by 1580 they were down to
one surviving grandchild - Elizabeth I
two great grandchildren - Mary Queen of Scots and Margaret Clifford, Countess of Derby,
four great-great grandchildren - James VI of Scotland, his cousin Arbella Stuart, and Margaret Clifford's two sons, Ferdinando and William Stanley.
Even of these, Elizabeth and Arbella were to die childless.
The same applied elsewhere. For most of the 15th Century, the House of Austria had only three or four male members, and between 1496 and 1500 Emperor Maximilian I and his son Archduke Philip were the only male Habsburgs alive. The birth of Charles V (1500) and Ferdinand I (1503) was partly offset by the death of Philip (1506) and Maximilian's death in 1519 put the family back to just two male members until Charles and Ferdinand had their first sons in 1527.
Dynasties are in a perpetual race between reproduction and mortality, and in those days mortality often won.
