I like her just fine. She's a bit overexposed with everything huge apparently swirling around her but I love her relationship with Tilly, Saru, and the Empress. My only thought is its weird to make the Stoic Spock-type as your dramatic lead. Still, I am looking forward to Season 3.
One of the stupidest things I've read is saying she and Mariner are identically "mean and unlikable" which is ridiculous because the two have diamatrically opposite personalities. Mariner is the mother of all extroverts while Burnham is so internal it hurts.