I wouldn't change a thing. Michael Burnham is the best thing to happen to the Spock character since the Genesis Wave.
Points for "Controversial Opinion".
Time for mine: While I think Saru would fit perfectly into the 24th/25th Century, Burnham wouldn't. Burnham is very much a woman of the 23rd Century. She loves to play fast-and-loose and trying to convince people to go with unconventional solutions. She's the antithesis of a TNG Era character.
When transplanted into a time like the 32nd Century, Burnham is the perfect kick in the rear-end that a decimated Federation needed. Someone from the 25th Century would be a character from the time when the rot that ultimately led to the way things were before The Burn began. The Federation became complacent, beauacratic, and stagnated.
I know that's not saying what I'm "supposed to" say like "
Discovery should've initially been set Post-
Nemesis!", but I just don't buy it. That's not the way Burnham's character plays, connection to Spock or not.
I also don't buy Discovery as a late-24th/early-25th Century ship. Sorry, but I don't. It doesn't look like some funky aquatic sea life, like most TNG+ ships look like. Hell, the original design for
Discovery was from
Planet of the -- fucking --
Titans. That was going to be a TOS Movie in the '70s. The ship design was intended for the 23rd Century and they even sneak it into the background in TSFS. It's part of the wreckage in BOBW, and presumably was an older design at the time, which takes us back to... the 23rd Century. No, I don't think Discovery looks like a
mid-23rd Century ship, I'll agree with people there, but it definitely looks like a
late-23rd Century ship. That's why I would've liked
Discovery being set Post-TUC, during a time when Burnham's type of attitude would be in its Waning Days but would still be there and thus would still work.
Whether by accident or by design (probably little bit from Column A and a little from Column B) the 22nd, 23rd, 24th, 25th, and 32nd Centuries all have a unique character to them, and you can distinguish between them if you know what to look for. Different parts of the 23rd and 24th Centuries have their own unique sub-characters too. When anyone says, "It's all the same!" it's just lazy and unobservant.