The main issue to me with the entire premise of "modern Trek" is just the cultural sensibilities the writers and directors have shifted to. When you think of anything from TOS - Enterprise, the idea of a Starfleet crew is in the form of highly trained, highly disciplined and highly competent individuals. These people respect the chain of command, the infrastructure of Starfleet and (generally) the rules. They behave how fictional soldiers should. Sure you have outliers and incidents that often become the specific focus of an episode here and there, but for the most part, the reason you don't have to counsel *everyone* on the bridge is because they are the "best of the best". And in order to get to even the first level of "best" they had to endure all that training, both physical and psychological and score highly to even get INTO Starfleet Academy. And those that were lucky enough to make it can still crack and wash out before ever graduating into actual ranked officers.
Where as now, the crews are less like officers and more like a small group of anime kids that go off on random adventures and get into all kinds of mischief. Burnham has failed upwards at every opportunity because she's good at everything and doesn't take no guff! That's not how traditional Star Trek characters have progressed through story arcs. And it's the same with everyone else always crying or jumping up and down like middle school kids. It's one of the flaws I don't expect to ever be "fixed" because I think for the most part it's "working as intended"
It occurred to me a while ago that my perfect model for a modern Star Trek series would actually be Marvel's Agents of SHIELD.
A tight-knit group of highly-trained, morally-solid (yet endearingly quirky and likable) professionals, with clear specialties, responsibilities, and a chain of command, being given specific missions, which they accomplish through a combination of trained know-how, scientific exploration/inventiveness, and surgically-applied violence. Complete with the "token alien/outsider" character (Skye/Daisy, Yo-yo, Enoch, Deke, Sousa, etc), and a good blend of episodic early adventures and season-long arcs that still manage to give every character time to shine.