Wasn't the whole point of TC to offer a different experience every play through? I know it's still just one map, but it was for offering a new angle at which to attack the other team a different way. Arena is no different, what's negative about 6 potentially different arena maps thrown into one? TC anything is just "CP/KotH/CTF that has 6 potential maps thrown into one".
The point of TC was to prevent players from anticipating the gameplay tactics they need immediately upon joining the map by providing random rounds; and to offer a map that would not "get old" as quickly as other maps... But:
When you change the objective setup you also change how close you are to achieving the original goals for TC. CTF (IE Shmitz's TC map) was about as close to the original goal criteria TC conceptualists had whilst also addressing stalemate issues of classic TC. When you take another mode you lean towards another style of play and criteria that less resemble TC and resemble those other individual game modes. I'm not saying it wouldn't work on some level, just that you'd be more productive leaning your project in other directions when/if you're gonna lean that far from the original TC setup. Because Arena is such a different mode from existing ones and attracts a particular crowd of players.
It's my belief that arena-TC would not make the most of the environments on offer to players with rounds so short and as an arena mode it wouldn't feel like TC only being allowed to spawn once a round. CTF or KoTH would provide a more close to the original game experience for TC; whether arena is functional or not. Though i'm usually one to advise people not to get stuck in old concepts that don't work 100% (and evolve those concepts), it works a little differently when you're combining 2 different official game modes with different gameplay and gameplay criteria.
What i'm saying is, if i'm saying anything conclusive at all, is that the community would probably be better off with 6 arena maps that could also be later converted to KoTH, than a single TC map that feels like a bunch of arena's thrown together and questionably address the "TC issue". Just because arena never stalemates does not make it a default replacement for the existing TC setup.
This is why some of the more experienced level designers (Shmitz, YM) have opted for A) the CTF style TC and B) A modified version of the original CP-TC. It's not just about making the mode functional, especially when choosing certain aspects to increase functionality sacrifice other core aspects of the game mode.