Besides not looking much alike, Madge Sinclair had a fairly prominent Jamaican accent while Sonequa Martin-Green's is from Alabama with a lot of theater vocal lessons suppressing it to play someone from anywhere in the US.
Not that either are insurmountable issues, mind you, but I agree with the others that it creates an uncomfortable situation when we reduce the already low number of characters played by people of color down even more by combining two of them into one for the sake of a minor continuity giggle for fans.
Plus, we don't know Burnham's fate as of yet. Discovery doesn't really strike me as a "And they lived happily ever after (until 30 years later when their ship was disabled by a giant whale-loving space robot Tootsie Roll)" type show.
I think the ridicule it’s being responded to with here is a sure sign that none of us want it to be a thing. Though in this day and age of badly thought out decisions, who knows. Given some errors of judgement in the entertainment world of late, we can only hope she’s not Uhuras cousin as well as Spocks adopted sister.