TOS: Scotty
TNG: Data
DS9: Dax for seasons1-3, Worf for seasons 4-7
Voyager: Tuvok
Enterprise: Trip
Bullshit, tho.
TOS never made any specific mention of who the 2nd Officer would be - all we have is conjecture.
DS9 never made any specific mention of who the 2nd Officer would be - all we have is conjecture.
VOY never made any specific mention of who the 2nd Officer would be - all we have is conjecture.
ENT never made any specific mention of who the 2nd Officer would be - Trip apparently was supposed to be Archer's second-in-command, that is, 1st Officer, until T'Pol rewrote the rules.
In every show, there were exceptions that never were clarified, casting doubt on the whole 2nd Officer deal.
DSC isn't doing any worse than these shows so far. Nor any better.
(TNG is the one that differs from all the rest, in making multiple explicit reference to Data being either "third-in-command" or "Second Officer".)
Pike only took command due to emergency circumstances in the premiere. At the end of the episode Starfleet made him the official Captain of the ship due to a combination of the Red Angel investigation and the Enterprise needing to go in for repairs. That's the whole reason why Pike where's his gold Enterprise uniform for most of the episode and switches to the blue Disco outfit in the final scene.
Good conjecture - but Pike's status changing is not spelled out. Instead, his treating the command as "joint custody" is the bit made explicit in dialogue at the end of the episode.
Then again, in "The Sounds of Thunder" Pike specifically addresses Saru as his "First Officer", making that bit finally clear. Similar dialogue on Burnham's current status is still missing.
Timo Saloniemi