Well she might have the right to waive counsel, but even if she had counsel she pleaded guilty to the charges. So striaght onto the sentancing phase. Now you might be able to try and argue that the actions after Georgioiu where down to emotional impariment but the mutiny charge is a little harder to get around.
She tried to subdue her CO and take command of the Shenzhou, after her CO decided not to follow her advice. She then also proceeded to lie that her CO had changed her mind.
The best result she could realistically hope for is for rank to be restored as for the Captain's chair that should be out of the question.
Is that like how Kirk, Spock, Scotty and Sulu couldn't possibly hope for the captain's chair after they literally stole a starship and destroyed it?
Anyway, restoring her to rank but barring her from command would be ridiculous on the face of it. Anyone with a sufficient rank can potentially find themselves in command if the situation goes south, therefore no one who is deemed permanently unfit for command should ever be allowed such a rank in the first place (pretty much anything higher than Ensign would be laughable, and I'm pretty sure we've even seen Ensigns in the position of taking command at least once or twice).
Either Burnham is forgiven by Starfleet (in which case, a Captaincy is no problem, even if it should realistically take some time before she can get there) or she isn't (in which case the best she can hope for is to remain a specialist outside the chain of command).