In "The Tholian Web" the Defiant crew wore the arrowhead
...Although the director made a damn good effort at hiding this fact: the extras playing the
Defiant dead were clad in standard
Enterprise uniforms, but they had their arms and torsos twisted so that the insignia were invisible. Save for just a couple of slip-ups, that is.
The same happened in "Ultimate Computer", where Commodore Wesley's custom uniform had the starburst/rosette insignia design, while his
Lexington crew hid their chests in every shot. No slip-ups this time. In "Doomsday Machine", Decker's crew was conveniently absent!
The design invented for "In a Mirror, Darkly" was a rather minor modification of the arrowhead, so one could pretend this is what we glimpsed in the TOS episode and mistook for the
Enterprise design because of poor image quality or something.
The arrowhead was also used Starfleet-wide in STXI
Or at least on the
Kelvin, the
Enterprise and Starfleet Academy. That's about as extensive as its use in TMP, but STXI did not feature competing designs whereas TMP had at least one alternate design, that for the Epsilon XI crew.
The old 70's Star Fleet Technical Manual said the TOS logos were for different branches of Starfleet, rather than different ships.
Said branches wouldn't need to be particularly big to make this work for TOS/TAS - they'd need to cover only the
Enterprise, the scout
Ariel, some third starship whose crew was spotted visiting SB11, and/or SB11 itself (because an office worker there wore the arrowhead in "The Menagerie"). STXI would add the
Kelvin and the Academy to the mix; one could still argue that the arrowhead was for the 1st Fleet, which included Earth, a few starbases and a few hundred ships, of which a couple were big cruisers - while another Fleet would perhaps include another major planet's SF installations, the
Exeter and a few hundred other ships, and so forth.
Timo Saloniemi