I wonder how they’d rationalize it. I think if they’d done this, they should have done it like an anthology where each character has the same personality but is canonically a different person, almost as if Boimler, Mariner, Tendi, and Rutherford were character actors.

The maroon uniform era would be complicated; you’d need to figure out how to set it far enough so that they don’t exist too close to either the TOS or TNG versions. I’d say the 2320s or 2330s ( roughly when Picard was in the Academy) so that they’re all retiring by the start of DS9.

I’m not sure if DSC era proper would work well as a setting for a Trek comedy - I’m not sure there’s enough to joke about for a whole season, and I think the overall tone of the 32nd century setting doesn’t work well for a comedy. However, either a pre-burn future (mid 25th-30th) or maybe a few decades to a century after Discovery when the Federation’s back on its feet might be nice.