So the shoulder tabs would show rank and division for everyone below RAdm but change to something completely different at that grade?
Not everyone, as none of the long-sleeve uniforms below flag rank use epaulets for indicating rank.
Not that the idea of "one star for the second flag rank" would be objectionable as such. Indeed, that's what the TNG S1 scheme seems to suggest, too. Commodore (or Branch Admiral, or whatnot) could have the broad sleeve braid of all flag ranks, but no narrow braid to go with it, and no star on the shoulder.
Leaving admirals without rank insignia for short sleeve uniforms? That doesn't seem likely at all.
In this setup, a short-sleeve uniform would simply have a different configuration, just as with the line rank uniforms. The one motif with TMP uniforms is a move away from the simplicity of TOS and towards seemingly needless complexity, perhaps in hopes of catering for the costuming needs of sequels. But if there's any logic there, it would be not duplicating the rank markers, always going for "OR" rather than "AND".
It might be different if we ever saw a flag epaulet, or a vehicle or doorway marking, with something other than the single star. But that's all we ever get - probably because TPTB wanted Kirk to stand out in the Headquarters scenes, and thus kept his flag uniform unique.
Like I said, all these alternatives sound terrible, and would be confusing to viewers.
But that's true of all things military. Most people laugh out loud when hearing for the first time that some poor sod has to bear the rank of "Vice" or "Rear"!
And this is supposed to be the future. There's also a "part of the audience" that knows the space technology relevant to the story, and enjoys the mixture of attempted realism and accidental or deliberate innovations and impossibilities... And another part that finds the innovations and impossibilities cool without realizing or caring that these are innovative or impossible elements.
The term [Branch Admiral] was used in "Redemption" (IIRC) but the admiral had normal insignia, implying it was more of a title.
"Redemption" featured Fleet Admiral Shanthi, with the three pips of Vice Admiral. Ditto with Brackett from "Unification", and Nechayev's final TNG appearance in "Journey's End". Odds are, then, that Fleet Admiral is not a rank as such, but a honorific or position applicable to certain flag officers, typically of Vice Admiral rank. (Quite possibly it could refer to officers in command of a specific Fleet.)
As a corollary, one might suspect that the five-pip rank in Starfleet is not Fleet Admiral, to avoid confusion, but rather something like Grand Admiral. After all, we have never heard Fleet Admiral being unambiguously used as a rank - that is, those words have never described a person whose rank insignia we would not recognize as belonging to some other rank. There has never been a five-pip Admiral on screen in TNG, either. And while the TOS movies featured several people with the rank pins corresponding to the five-pip rank (Morrow, Cartwright, Admiral Bob, Admiral Bill), none were addressed by rank.
Timo Saloniemi