I think you completely missed what the writers were doing with Burnham. She was a very competent person who became so convinced she was right and that she was saving lives, she ended up making a huge mistake. The mistake was the mutiny.
I think we can all relate to a person who feels they are doing the right thing, but end up screwing it up. After that we see Burnham's redemption. That is a story to which we can all relate. I think your dislike of Burnham clouds your understanding of the character.
To me, Burnham is easily the better lead character between Mercer and Burnham. Burnhqm had by far the most compelling storyline. About the most interesting thing about Mercer's back story and season 1 story was his relationship with his ex-wife.
Her mutiny, subsequent redemption, and reestablishment of her position as one of the best officers in Starfleet, made her the most interesting character on DSC despite my belief that SM-G's performance in season 1 was the least great of all the main cast (except Mary Wiseman).
But, bottom line, these two characters cannot reasonably be compared. One is the lead on a show that stresses comedy, and the other, on a show that stresses drama.