It's not clear to me that splitting up Boeing in commercial+business jet, defense, and space would make it more ineffective than its current incarnation? Boeing's ability to purpose build commercial jet frames for defense applications both seems to be... a) not performing well (see KC-46), and also b) not a future growth industry with the focus shifting to the Indo-Pacific and peer conflict (given the vulnerability of these types of platforms).
It's not a technical problem. It's that they need to stay too-big-to-fail, to be able to resist the very aggressive competition of other aircraft manufacturers. If they are broken up, the smaller companies would not be able to compete effectively, and they would also be immediate acquisition targets by largely foreign competitors.
I agree with others here that think they need to be a quasi-government-run company, but in the US that is done through oversight, managing the manager rather than stepping into the management role directly. Of course we have to absolutely gut that awful management with extreme prejudice, to start.