The two jobs are not the same shape
New business selling is episodic. It has a beginning, a push, and an outcome that is visible within weeks. Account management is continuous. Nothing dramatic happens on any given Tuesday, and the results appear months later as an absence of churn. Because urgency always beats importance when both sit in one calendar, the continuous work gets postponed in favour of the episodic work, over and over, until a renewal is missed and everyone is surprised.
That is the real argument for separating the roles, and it is an argument about attention rather than about personality types. The hunter and farmer language obscures more than it reveals. Plenty of good closers are excellent with existing customers when the time is protected. Very few are excellent with existing customers when their quota is behind and month end is on Friday.