Re: Starfleet Starship Insignia was all supposed to be the same?
Now, as to why some starbase personnel might wear the arrowhead, that's a different question.
Regarding TMP, that's the issue, yes.
And, given that the arrowhead had apparently crept into the starbase area, so that Kirk isn't wearing a flower at first, why not also every area, including Epsilon IX as well?
“A life is like a garden. Perfect moments can be had, but not preserved, except in memory. LLAP” — Leonard Nimoy (1931-2015)