In what way did Chakotay and Mayweather not have a purpose? They weren't just totally bland character like Kim or Tuvok, they were quite flavoured (a rebel and a cargo dude born in space!) but the actors couldn't make the roles come alive. And when somebody doesn't give a shit like Beltran and whines about how ridiculous the only show he will ever be remembered for is I have the audacity to point out that such an attitude is the main reason for the failure of this character.
These actors were no George Takeis, never getting a chance to shine until they actually get something to do in the end (TUC). They had their chances (the two Mayweather shows Fortunate Son and Horizon were fairly well written) and blew them.
Their bland because those aspects you mentioned are hardly brought up.
Chakotay was supposed to be a rebel, but the writers didn't want him to undermined Janeway, so he was written as a one dimensional Native stereotype instead and Mayweather being born in space is hardly brought up after the first season.
You can't set up interesting things about characters and then ignore them and expect people to like it.
If it's about the characters, what do you need a spaceship for? It is a simple truth that people are what they are becauee of their environment and act the way they do because they are carrying out social roles suitable to it. Science fiction as such rather conflicts with realistic characterization.
If it's about characters having bad ass moments and vividly presenting themselves and changing in a satisfying way? If it's about heroes suitable for vicarious fantasy? Then there have to be victims, sidekicks, admirers, satellites, characters who do the unpleasant stuff.
The best example is the much abused Harry Kim. Kim was a token Asian mainly. But insofar as he was a character he existed first to service the Tom Paris character. In The Caretaker, Non Sequitur and The Chute his role was to be saved/redeemed by Tom Paris. And the rest of his function was to do the unpleasant stuff, like wanting to go home or being otherwise flawed, as in Favorite Son or Nightingale. The Kims have to be written so that there can be episodes or scenes that aren't about badassery.
I never said its all about characterization, but characterization is an important part of fiction. Really Harry Kim whining and acting like a pathetic child is not the way to have character the audience is invested in, it seems like you could have given his roles in stories to random Gold Shirts and you wouldn't miss anything, a random Gold Shirt can whine about not being home just as well as well as Harry can.
If Harry Kim never had that character were he does something amazing and gets promoted and deals with having new responsibilities, then what's the point of the character? Nightingale showed that he is a just a pathetic mamma's boy who is upset because he is not as special as mom said he was and screws everything up. Why should I care about a character who never seems grow or learn from his experiences?
He never goes anywhere as a character. He is the green ensign, start to finish.
And really victims, sidekicks, admirers, satellites, characters who do the unpleasant stuff, should be guest stars or reoccurring characters, not part of the main cast. Harry Kim might have worked as a reoccurring character, rather then someone who shows up every episode.
Plot and setting are important, but you can't just ignore characterization, flat characters have dragged down the last two star Trek shows.