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.
Not really. Mayweather was an empty shell before those episodes and they did nothing for his character in the end. He really wasn't a character, anyway, but more of a glorified extra, truth be told. TOS did far more with Sulu and Chekov in comparison. Mayweather was more interesting when he was originally conceived as "Lieutenant Joe Mayweather" during the early development of the series, but essentially all of his character attributes were transferred to T'Pol, leaving him only as that guy driving the ship that rarely says more than "aye, sir" in most episodes.