American beeches only produce a single flush of growth per season. Asian and European varities produce more and are more vigorous in general--more akin to hornbeam (which are relatives) than to American beech.
I have been surprised to find that the beech and the hornbeam are not that closely related.
Beech is from the Fagaceae family including such trees as beeches, oaks, and sweet chestnuts. While the hornbeam is from the Betulaceae or birch family including such trees as
birches, alders, hornbeams, hop hornbeams and hazels.
Although both of these families are in the order Fagales which contians 8 families Betulaceae, Casuarinaceae, Fagaceae, Juglandaceae, Myricaceae, Nothofagaceae, Rhoipteleaceae, Ticodendraceae
Betulaceae or the birch family is actually most closely related to Casuarinaceae or sheoaks than the beech tree
with the beech being one of it's most distant relatives in this order
Anyway... Not sure I like where you have gone here but I would like to show a couple of pictures of beech that are in the more conical shape to show that they can and do grow like this. It is more common in trees less mature but still a valid shape for a younger vibrant tree of this stature. I would say that growing them in only the more rounded broom style has more to do with Bonsai fad than the form of natural trees.