But what we DID see, for a while at least, was a lot of people sympathetic to that subreddit arguing in any way they could think of that the ban was either inconsistent, not needed, unfair or wouldn't work. But what do you know, by and large that content kind of just went away.
So it wasn't necessarily the ban that got rid of FPH but rather the "Fat Acceptance Movement" losing steam.
I guess your argument for the decline in activity not coming from the ban, but scaling up and down in relation with the prominence of fat acceptance, would have to be that the ban coincided with fat acceptance losing steam around the same time, which I don't think to be the case. (It's also a way of talking that seems to equivocate on whether the behavior was acceptable, since it can be explained as a response to something else, and I think its unacceptability is important enough that it needs to remain clear in any conversation about it.)
I don't have an obvious way of measuring the relationship one way or other. But the face value version of events, which is just that the ban worked, full stop, requires fewer coincidences.
(inb4: "found the Walmart shopper"!)
There are plenty of people who thought that it wouldn't work to that extent, either. They claimed that allowing a subreddit for toxic topic X at least had the benefit of segregating proponents of X; and that if such subreddits were banned their inhabitants would infect the rest of Reddit. But that didn't happen.
I remember when posts from r/FatPeopleHate would regularly make the front page. Then FPH was banned, and you know what, we didn't see it metastasize elsewhere, we just saw many fewer FPH-style posts, which I'd say is a good thing.