This will be one of those "just 'cos we didn't show it, doesn't mean it wasn't happening..." kinda things. You know how much they do that...
In truth, it was a bit convoluted in the episode and there was either confusion by the writers (or just sloppy writing) regarding the difference between an officer being appropriately qualified to take on the acting "command" role and the career progression of an individual officer to the substantive rank of
Commander -- clearly not the same thing.
It was patently obvious that numerous more junior officers than Troi had been taking post as officer-of-the-watch/day/deck (whatever Starfleet cares to call them). Presumably, all of those had already been passed for acting command at some point along the way but Troi had, for whatever reason, progressed to Lieutenant Commander without ever having qualified for the command role. It wasn't made abundantly clear in the writing but the implication was that (as a non-Command officer) Troi was not in a position to progress beyond Lieutenant Commander without so qualifying. Obviously from a story point of view, it nicely tied back to previous events where she *wasn't* sufficiently experienced or qualified.
I agree that it's a bit dumb that they just couldn't get on and establish which characters held what role on Discovery. We didn't necessarily need to even see or meet them, but positions like chief engineering officer, chief medical officer, second and third officer all eventually come into the story at some point and, as they had clearly abandoned the whole "it's not about the captain and senior officers" concept (which later became Lower Decks), it served no purpose not to clarify this. I totally get why some folks really just don't care; that's fair enough, it's not a massive deal nor is it particularly essential to the story, but equally there's no particularly good reason for them to avoid clarifying things either.