Genuine question - what stops them just hiring writers not in America?
Are you talking about books specifically, or all writers? If we're just talking books, probably nothing.
On the large media scale: American audiences tend to respond best to American writers. While there are many cases of international movies and TV shows being accepted here, by and large we like our entertainment to be home grown (or at least close enough that we can pretend it's ours, i.e. Canadian). Having no American writers wouldn't stop Disney completely, but it could still hurt them.
On the medium scale: It's important to remember that Disney owns ABC. There is no way ABC could stand against the other big US networks without American writers. FX and the various Disney Channels would also struggle. And there's no way Disney could take that hit when their movie and theme park industries are reeling.