When the whole point of the ship is to do engineering marvels, the CEO would appear to be a key character. But during S1, we don't need to believe in the existence of a CEO: none ever got mentioned!
The absence of the CMO is excusable, and an example of how this new thing could work: the medical emergencies and plotlines of the S1 episodes only ever involve the personal physician/lover of Stamets, for the in-universe reason of Lorca wanting it that way. There is no contradiction in the CMO being offscreen, and we can freely choose to say that he was the full Commander we glimpsed in "Magic to Make".
S2 is where the thing breaks down. Engineering is no longer exclusively about spore magic. A CEO is referred to several times but never shown. And the ship is bursting her seams from excess engineers of high rank, none of whom is the CEO!
Also, medicine is no longer about Stamets exclusively. But this isn't a problem: we now get medic characters who could hold the CMO status, while the medic of interest is dead for much of the season and recuperating for the rest. And we stop getting references to an offscreen CMO.
S3 involves reshuffling the now all-volunteer crew, and it makes sense to assume Culber is the CMO now, him being the highest-ranking whitecoat and all. But things only get worse as regards the CEO business, now that the high-ranking Reno is a full-time crew member but rarely does any work and never commands, and Stamets still refuses to be the formal boss while nevertheless ordering everybody around.
Trek in general doesn't work unless the main characters are the bosses, because in Starfleet the bosses do everything. Or if we want to look at people who do something specific rather than everything, we still need to acknowledge the bosses, as in Lower Decks. DSC sorta managed for a single season, without actually trying much... But it's been a dismal failure ever since.
Timo Saloniemi