I agree that she is not a great character. I'm just commenting on the implication that Burnham has never been in a position that she needed someone else to save her.
I've often said (on the DIS, where maybe this belongs) that my main problem with Burnham is that she's always off doing things herself without involving the rest of the team. It's like she sees a problem, and instead of getting a group of smart Star Fleet people people together in order to figure out how to best address the issue, she just ducks out and attempts to solve it herself.
Granted, this is also identified as an in-universe criticism of Burnham, as Spock has lamented to her that she does not need to carry heavy burdens by herself, and that she should allow others to help her solve problems. However, that being the case, I think it pains me more that it seems the writers intentionally WANT her to be this way.
The best part of an ensemble cast TV show is the way the ensemble works together to solve a problem. That working together plot device can be a way to show chemistry among the main characters, and allows for fun a clever dialogue as the bounce things off of each other in the process of solving the problem the plot has presented.
But Burnham's need (again, seemingly intentional by the writers, unfortunately) to attempt to shoulder the burdens and solve problems by herself, practically shunning others, really tears apart any hope to grow that chemistry among the cast of characters. There is some chemistry among the rest of the crew, but it either does not include Burnham or it does include Burnham in a forced and non-organic way. The way to make it organic is have Burnahm be an intrinsic part of the entire gang when problems are being solved.