Because the Spock-Sarek relationship for decades has been about the issues of how Spock made a choice to join Starfleet in order to go his own way. That his rejection of the Vulcan Science Academy is a moment where Sarek has to project Vulcan stoicism and disdain for an “illogical” decision, but on some level you get the sense that he respects Spock for bucking what was expected. But all of that is left unsaid, implied through the acting, and remains a major relationship issue within the franchise for decades.
When you shoehorn Burnham into that, and basically have Sarek screw over her application to the Vulcan Science Academy in order to favor Spock, I think it robs all of what was left to nuance and ambiguity, and underlines a definitive perception on those issues in an awkward way.
Also, I think part of what makes Spock’s upbringing tragic is the idea he only had his mother as a touchstone for his humanity on a planet full of Vulcans. Inserting Burnham into their family dynamic diminishes that idea.