Well that's what happens when you put fads and pop culture references in TV shows. They can become pretty dated pretty quick.
I mean, imagine if one of the shows were to praise someone like, oh idk Elon musk.... Oh wait...
My headcannon is that like many things over the years, sports will come and go, and this is the new "retro thing that become ironically popular, then became legitimately popular again"
And the engineers just happened to discover an unused space that perfectly fit those dimensions for the lanes, and DEFINITELY didn't make the lanes the very first consideration and design the ship around them....
By the way, if you want to know whether or not this is canon? It's canon.
In 2266, Kevin Riley, under the influence of polywater intoxication, "ordered" a formal dance to be held in the bowling alley on the USS Enterprise. (TOS: "The Naked Time")
I bet it didn't survive the refit. Actually, I suspect that's where the "Rec Deck" from TMP ended up, though I have no proof (were the post-refit blueprints ever published?)
Is there even a space for the "Rec Deck" to fit in a Constitution class? I don't think it would fit where the blueprints show the bowling alley because the "Rec Deck" is at least two decks tall. The Constitution class is surprisingly small; I was a TNG guy and the Galaxy class ships are comically gigantic.
Would be a question I would pose to a Youtuber by the name of We Travel By Night, who has tackled things like "The turbolift shafts on the exterior model don't change from movie to movie, but the turbolift doors gradually move apart as they update the set." or "the ship's neck is so narrow that there's no room for the turbolift and the engine plumbing to pass by each other, so how does that even work?"