Don't see the issue, though. It's the ICONIC ship in the series, why would it be a problem if people are attached to it? isn't that what they want?
And why is the Excelsior any different? If they're hung up on the era, it's about the same. And the NX-01 is in game at same level as the TOS connie, but they don't have issues there. And the Vulcan ringship (ENT era) is flying around at endgame, no issues there.
Speculative explanation: because the Constitution is too old.
Wait before you launch into a rant about other Ships being as old and used at T5...
Not in-universe old, IRL old.
All the other ToS-era Ships are either from the movies or have been adapted to fit TNG-era visuals, the Constitution (especially the pre-refit one, which I guess is the one you'd want?) has not. So, its "crude plastic model" design wouldn't fit amongst a bunch of "CGI-drawn" designs. It'd look jarring.
It does when you fly it at T2, and that's the post-refit version.
Why not just use the Sovereign? If you think about, it's actually more visually similar to a (much) more streamlined Constitution than to the Galaxy.
Anyway, I've got a bad feeling about the Fleet Ships.
First I heard of them, I thought "cool, Ships that can be earned and rival C-Store Ships!"
Then, it was "there are 2 versions and the good one requires a C-Store token."
Now, it's "there's only 1 version. The other option is for those that want to fly lower tier Ships at T5 without giving up too much (Saber-R, that kind of thing), not actual upgrades over those obsolete RA Ships you're using, dirty peon!"
So yeah, sounds like MOAR P2W. Will wait for the final release.