This is the way I picture it:
If Fuller wanted each season of Discovery to take place in a different era with a different set of characters, then it was only going to stay in the TOS Era for one season. He wanted it to look as much like TOS as possible. If that didn't go over well, then no big deal because the next season wouldn't be like that because it wouldn't take place then.
Then people above Bryan Fuller said, "We don't want to do all that! It sounds expensive! Set the show in one time-frame with one set of characters. Just stick with Kirk's time." Then Bryan probably said, "Okay. Not a problem. This is what I want to do. This is how I want it to look." Then CBS probably said, "No! You can't do that!" Then Bryan might've replied with, "But I thought you said you wanted the TOS Era." To which CBS would reply, "We want our own version of Star Trek. The Abrams Films are hot. The TOS Era is where it's at! But they updated the look! We want you to update the look too! But make it look different from the update JJ Abrams did!" Then Bryan might've said, "Okay, but..." CBS getting frustrated might've said, "Stop arguing. This is what we want you to do. Go ahead and make it happen!" Then Bryan might've replied with, "But isn't that a reboot?" CBS getting annoyed would say, "No! We're doing the Prime Universe! That's what makes our Star Trek separate from Paramount's Star Trek!" Bryan muses, "But if it's not the same, then it's a reboot!" CBS snaps, "IT'S A VISUAL REBOOT AND IF ANYONE ASKS THAT'S WHAT YOU'RE GOING TO TELL THEM!!!! Now get out of my office!!!!!" Then Bryan left. To fight another day. After which he left "to focus on American Gods."
This would explain CBS's point of view, what Bryan Fuller probably wanted, and what we ended up with and why.