Trek, as we all know, is about seeking out new life and new civillisations. It is not about seeking out new life and waging a war to rule the galaxy or surviving in a post apocalyptic world overrun by zombies.
I don't think anyone is suggesting literally changing the subject matter of Trek to match those shows, just doing something in the same style, eg instead and adventure of the week and move on, have a season-long storyline and cast the net wide to focus on a large group of characters, some of which don't even meet others as opposed to the same seven guys week after week, some of which don't even really get anything to do.
There is no one like Harry Kim or Travis Mayweather in the main cast of Walking Dead. No reason why they should be in a Trek series either.
Actually, what would really help this show is if the characters for the main cast are actually people the writers have arcs and character development for, as opposed to what Voyager and especially Enterprise were guilty of which was basically filling a starship's staff, and that's who we'll be following.
I agree we need fleshed out characters but I'm unsure about abandoning the episode of the week format if the series is set on a starship. Long story arcs worked extremely well for Deep Space Nine as it was set on a space station. The characters couldn't just move on to the next planet. They had to stay there on DS9 and deal with the stuff that came at them.
I'm not sure I'd like a Trek series in which some of the main cast don't interact with each other. I enjoy the Trek format of a united crew dealing with the same problem. But it could be an idea to set the new series on a starship and a starbase or even a planet too. 2 or 3 locales could open up some story possibilities. It was never Trek's formula I had a problem with. It was the recycled and lazy episodes that didn't offer anything new.
I fully agree the new series should not have any passengers along for the ride like most of the Enterprise cast and half of the Voyager cast. Every character should add something vital to the cast.