I want to address this from a different vein which is why I think Burnham seems more like a mary sue then say kirk or picard and it comes from an element of the show that I think sounded better in theory then it did in execution which is making a non-captain the lead character.
With Kirk/picard/etc they are the captains of the ship so we expect them to have all the answers, know what to do, etc. or seek out appropriate advise. The times they have to go against authority it is often an admiral or somebody light years away who doesn't know the reality of the situation.
Now in discovery we have a different dynamic. Our lead character and the one who is the hero and is going to save the day isn't the captain. So for her to be right and save the day she has to be the one to come up with the ideas and not the captain and in come cases (like the mutany) have to actually go against what the captain wants because she is the one that is right. I think having a non-captain in this role makes her look more like a mary sue then if it is the captain making all the right decisions. It almost comes accross more like Wesley (who absolutely fits this category) who performs better then all the starfleet officers on the ship. With Burnham she was starfleet but after we get past the pilot she has no rank anymore but is still the one with all the answers.
I don't want to get into who is and isn't a mary sue, but I think Burnham not being the captain and being in the hero role makes her appear to be more of a mary sue then if the same character was the captain.
Honestly, I don't think the idea of having the show center around somebody not the captain really worked as well as it sounded in concept but that is a totally separate discussion,