I think Burnham is essentially heroic, yes. She has made a lot of mistakes, but so did Kirk. So, where does the line get drawn?Hey you keep asking question and expecting answers which I give, but you won't answer any questions I ask you. That is your rightI judge Kirk by the entirety of what I've seen and Burnham the same. He is essentially, again in my opinion, a good man. A good captain.
Because, Kirk was insubordinate, assaulted Starfleet officers, wrongfully imprisoned an officer, broke a prisoner out of jail, stole Starfleet property, destroyed Starfleet property, offered a false flag of truce to Klingons only to kill several Klingon soldiers (a violation of the Geneva convention), stole Klingon property, committed an act of war against a sovereign power, among others.
Where is Kirk's "anti-hero" status?