Why would you want a TDM mode? In a game with high time to kills the absence of an objective focus just helps encourage things to move a lot faster. This is basically TDM where it's essential to kill people to win the match, but if you don't move and play around particular spaces you will lose.
Apex TDM would be horrendously campy. People sat on rooftops poking and healing away at each other. The time to kill basically neccesitates something that pushes people together. Or perhaps very small, close ranged maps but that wouldn't be a good fit for many characters and weapons.
Ok: I'll rephrase it then - I want a version of Arenas where I can respawn. I want the non-goal-oriented aspect of arenas without the starting/stopping/buy phase.
Control works well when you're playing with friends who are rolling together as a squad, but I've found works much less well when playing with randos. And even when rolling with a squad, 2/3rds of your 9-person team will always be randos. If the mode allowed people to create custom teams up to 9 people (or backfill the remaining slots if fewer than 9) then I'd probably feel different about it. As of now, it's easy to fall into cycles where a team is fortified in an area, no one is pushing together as a team, and no one is choosing characters who can counterplay. Things get worse when your team is down in the first minute, and half your team drops out which I've seen happen. Making a game where it's just, "Hey, just get kills" may lessen the likelihood of people just quitting.
Make the TDM map small enough that it's hard to camp for long. If a couple of people still want to hang out as far as they can with G7s or Sentinels, fine - I'll take my chances with that.