You made a lot of overgeneralizations. Speed BE can be used on any fast enough paradox mon. For instance, Roaring Moon often runs BE Attack because of its stats and how it is fast enough to outrun nearly everything with a single DD anyways. However, BE speed Moon is still perfectly good. And so on. There is no good reason to look at the versatility of BE and pigeon hole it into a single boost type per mon just based on what you think is most popular.
Nor is there a valid reason to claim boosted speed tiers as something that only impacts HO, as if faster mons than Iron Valiant like Ace, Meow, or Pult (or Valiant itself) are never used on slower paced teams than HO. That simply isn't true. Speed tiers impact every team that actually engages with them with even a single mon. So, basically everything besides full on stall.
Roaring Moon in general has a lot more set diversity than people give it credit for. Boiling it down to only one "most controversial set" isn't really an accurate representation of its capabilities. It wasn't that GF suddenly got new capabilities when it was banned. It was that the DD sets were more properly explored by then.
I don't care to argue with you about how much each banned Paradox mon, of which there is certainly more than 2, may or may not have been because of BE, and if so, what fraction of the blame we are hypothetically assigning that. My point was that even if it was only Gouging Fire and Roaring Moon as you say, it would still be sufficient for at least an argument. We banned Shed Tail with only two abusers after it was found that Cyclizar wasn't the only one broken with that move. But more than that, the BE discussion goes beyond only the individual mons just as you claim Sleep does.
The reason why I glossed over the differences between sleep and BE, while acknowledging they do exist, was because the perfection of the analogy was never the point. This is a mechanics discussion. Calling BE only an item ignores all the points that had been made prior in that discussion discussing the very real impact of BE from an actual mechanics standpoint. You can agree or disagree on the alleged health of said BE impact, but it undeniably exists.
Sadly, that's how it goes a lot of the time. The community can be a bit volatile with opinions. Interest in a various topic is also not guaranteed. We have far more engagement from troll bait Uber drop discussions than we did for, say, discussing Gliscor counterplay leading up to that suspect. In the end, people will talk about what they want to.
This is just the tip of the iceberg on what Moon can do with the various DD sets.
