I can't speak for anyone else, but for me, it's not that I find it shocking Burnham is his adopted sister. I simply find it to be a bad decision to tether the lead character of a brand new series so tightly with one that is arguably the face of the entire franchise. Out the gate, the show is telling me that she needs that kind of help to make a connection or bond with the audience instead of allowing her to be her own creation. And since the show is essentially HER series, it's telling me that the producers don't believe in the show enough to stand on its own two feet.
For a comparable situation of bringing the franchise back to tv, look at TNG. Not a single character had a connection to TOS. With only a couple exceptions in season 1, TNG had no connections to TOS, which was something Roddenberry wanted. And on that decision, I fully agreed with... it gave TNG a chance to shine on its own instead of relying on past work to elevate it.
The result? By many metrics, TNG became the most popular series in the franchise.
The result of DISCO? It's probably the most divisive series in the franchise, even almost a year after it ended.