Because Wizarding World is better because it fits the more localized story of Harry Potter.

Probably because there hasn’t really been a successful spin-off of Harry Potter. When people think of the Wizarding World, they are really thinking of the Harry Potter stories.

I think that Harry Potter Universe just means the 7 books with Harry in it.

Wizarding World could mean Fantastic Beasts or any of the Harry Potter Games like Hogwarts Legacy or Hogwarts Mystery.

Not everyone who has read Harry potter or is interested in it has seen the fantastic beasts or cursed child

But almost everyone who are interested in fantastic beasts has read Harry potter.

So someone who is looking for the fandom is more likely looking for the HP fandom not wizarding world

"Wizarding world" may actually be slightly more accurate and encompasses the stories that don't feature Harry, but "Harry Potter" is the term I think most people will be familiar with/likely to look for. (and as @GreatMistress mentions, most people who read Fantastic Beasts will have read Harry Potter, and not so much vice versa. The other series/books kind of stem from Harry Potter, so using the term "Harry Potter" makes sense for this, I find.)

I mostly agree with what everyone else has said, with the addition of Wizarding World is sort of vague and could be related to any fantasy wizard world that exists outside of the Harry Potter Universe. Harry Potter is very specific and identifiable for a wider audience, with the caveat that it doesn't roll off the tongue as well.

Personally I don't think the turned-phrase "Harry Potter Universe" will ever be outclassed by "Wizarding World" for this reason. However, at the moment it is certainly branded this way, with the rebranding of "Pottermore" to "Wizarding World" and the "Wizarding World Fan Club." So even with the fact that it's vague and conceivably too all-encompassing, it just happens to be that this is probably the direction it will be headed anyway.

Right now the powers that be are certainly trying to expand the universe beyond Harry Potter. If they stick with just Harry, then there are really only seven stories that they can tell. They want to make Harry Potter into an MCU style franchise, so they’re trying to rebrand as Wizarding World. They haven’t really been successful at making a non-Harry Potter story set in the Wizarding World though. At least, not a popular one.

@Icecreamdif I hope there are many awesome ways to create a meaningful story set in the Wizarding World. I also keep the hopes high that one day 'Wizarding World Universe' will surpass that of MCU and DC.