Wow, that's interesting. Even among devoted fans of the show, she's not most people's favorite character. I have nothing personal against SM-G, but the general consensus seems to be that Burnham comes across as having a somewhat limited emotional range, mostly focused around "dour," and that her capabilities, motivations, and decisions have tended to be a little too obviously driven by the needs of the plot. What are you seeing that gives you a different impression?
This wasn't aimed at me, but I'll jump in and say that SMG's performance makes the show for me. I find that she shows amazing range and subtlety. For instance, the play of emotions in the elevator scene between killing the captain and stepping onto the bridge--it's a remarkable piece of acting with so many layers.
I also find that she's had an exceptional arc for a single season of Trek, and I loved how her major turning point was something as simple as "Whoops, now that I see these Klingons in their home environment, I can't hate them!" which tells us so much about why she made prior decisions, and the Trekkian humanity she embraces. I don't find her arc inconsistent--I find that she's got a lot of baggage--bias against Klingons, childhood trauma, a lack of socialization, etc.--and we get those layers pulled back one by one. Even when we think she's fixed herself around the middle of the season, she's still operating from a place of xenophobia that she has to roll back, beginning when meeting the Klingons in the MU, developing when Lorca reveals himself, and finally actualizing when she visits Kronos.
I do think at times her performance is better than what's she's given, and I'd love to see SMG get to play a wider range (she's clearly capable). But on the whole, the fact that she travels such a distance to the Burnham who smiles at the end of the season pleases me. I find her story sensibly plotted and realistic, even if some aspects of the season moved her through parts of her arc too quickly or slowly.