Likability is subjective of course. When it comes to Discovery, Lorca was supposed to be unlikable, but I didn't hear many complaints about him from the fandom menace crowd, and if there were it was more complaining that the "woke social justice warriors" were making another white male character out to be the villain. But I don't recall hearing much frustration with the Lorca character for that character's actions. There might have been a little more guff given to Emperor Georgiou, but once again, I never heard too much about people not liking her character per se, but some reluctance to soften a "Space Hitler".
Burnham not being likable was not the intention of the writers. They were desperate to make the character so cool and likable that it did the opposite on the internet a lot, even though some of the spite she stirred up was dripping in racism and sexism. That being said, the writing for Burnham was clunky at times. Though if Burnham had been a white male I doubt there would've been any charges of said character being a "Space Jesus" or "Gary Stu". This crowd had little to say about Jack Crusher or the legion of white male Chosen One characters in entertainment stretching back decades by now, even some literally called "The Chosen One" like Anakin. However, when that praise and "lazy writing" is given to characters they aren't used to seeing getting it, and maybe don't believe deserve it, now it's a problem.
Unfortunately, Burnham was never going to be widely embraced. Nichelle Nichols's Uhura is beloved in part because she was a glorified side character, who was a secretary/phone operator, that allowed some in the audience to pat themselves on the back for their racial "tolerance" and "enlightenment". That had nothing to do with Nichols's performance, that was just the way the character was written/used, and she did the best she could to work within the constraints. Zoe Saldana and Celia Rose-Gooding were given more to work with, and they still could've-should've-been given more. Uhura basically as attractive wallpaper was fine for some.
Burnham being the focus, being the best, being the one that was wanted, that was needed to save the day like we've seen with James Bond, Ethan Hunt, Jack Bauer, Captain Kirk, and so forth was too much for some. Sure, the writing could've been better at times. If I had had my druthers, she wouldn't have been Spock's sister, I would've tamped down on various characters gushing about her and just having her actions do the talking and cut out a lot of the heart-to-heart crying scenes.
But Burnham was never a Mary Sue. The series opens with her mutinying against her captain and starting a war, and she spends a good deal of the first season clawing her way back. There were personal heartaches and setbacks along the way after too. And she got pushback when she made it to the future. There was no endless praise choir for her. She had to earn her place. Like I've said before, was all the writing good? No. Could've they have given her even more challenges, or had her fail even more than she did? Yes, but the same could be said for all other franchise leads. Jean-Luc's failures were a bone of contention on his series I would argue. I definitely didn't like the sad sack version we got of him in the first two seasons.
Did I love Burnham? No? But I thought that Sonequa Martin-Green did a good job with what she was given.
apparently her shadow was long and I didn't watch those episodes of Saru and others handling things.
