The "they can do what ever they want with their private property" argument doesn't matter. This isn't about what they can do, it's about what should be done.
No nothing should be required of these organisations. But their products serve humanity. They SHOULD have a sense of moral obligation to do the right thing. As should we the people have the responsibility to hold private monopolies to high standards so as that they help most people (not just shareholders).
Apple controls a negligible portion of the desktop market. Microsoft absolutely dominates. Anti-trust is about protecting the free market from natural monopolies, and Apple is by no means a monopoly. A walled garden? Absolutely. But not a monopoly.
This is USA where private property rights are supposedly important despite government's attempts in other direction.