To echo Ilan Goldenberg and Shawn Brimley, I think it would be a disaster for the next President to appoint a Republican as Secretary of Defense. The symbolism — a combination of “Democrats can’t handle defense” and “Democrats don’t care about defense” — just sucks.
In general, I’m not so high on the idea of appointing Republicans to anything, but you especially want to keep them away from the national security realm. Now it’s a different matter to give an appointment to someone who’s an ex-Republican (or willing to become one). Actual party switchers who are willing to publicly articulate a narrative about switching are a valuable commodity and people like that should be shoved out in front of the camera whenever it’s plausible to do so.