While the halberd’s blade offers a lot of options for hooking your opponent, it equally gives them an opportunity to hook your polearm and manipulate it themselves. The simpler spearhead is also lighter than that of a halberd, allowing for more sustain when fighting for long periods.
I would definitely prefer a halberd (or billhook) over a spear given the choice, but it’s not as much of a direct upgrade as you might think.
They actually did that with birds!
https://americanornithology.org/american-ornithological-society-will-change-the-english-names-of-bird-species-named-after-people/