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My only major critiques for Discovery are that they walked back a Calvin-verse reboot after fan backlash (my interpretation), and that the theatrics usually don't mesh well with the action-oriented flow of the rest of the episodes around it.
The reboot thing was, to me, overly clear with the changes in aesthetics and technology. Especially the Klingons. And I get it: it's hard to dazzle audiences through vibrant creative direction, with decades of canon on your back. All that older stuff has compromises from old effects tech and budget baked in, so breaking from it is incredibly tempting. But the fans will not let you do this: just ask the Dr. Who production people. So we get some really oddball stuff happening in the first few seasons.
To the latter point, we get moments like: "The ship is going to explode in one minute, so let's argue for at least ten before we deal with that." This kind of thing happens a lot in Discovery and a binge-watch would have you thinking that the ship's counselor is either dead or contemplating transporter suicide. The dissent between characters feels valid most of the time, but other times is just jarringly out of character or contrary to self-preservation as to break suspension of disbelief. But there's usually angry, loud, arguing dissent. Which is a shame since these same episodes are hitting the mark on every other metric, IMO.
My response to the first five episodes was very much "It's like the writers are justifying a councilor being on the bridge crew."
To be fair, other characters step up to fill the void, but it's too little, too late.
Gene had a rule for TNG that conflict should not be between the crew. There are a few exceptions, but it's pretty consistent. I think that limitation made the writers more creative and greatly enhanced the series.