The problem with AI admins: they will blackmail you, if you will try to unassign em. I dont know about any bad sides of using AI cores while you dont try to remove em, but in roleplay terms it is a little bit scary to have entire sector controlled by the robots.
Personally i like to invest 1-2 points into the skill, which expands base limitation, but it is not nessessary, because you can manage colonies over your personal limit. It will cost you some stability. It can be raised by the last skill in the leadership spec. Also: you will have like 15 stability anyway, so, you have possibility to sacrifice some. On the other hand: enabling freeport will cost you 3 stability, so, it is up to you how you spend it.
Also: didn't know about Nexerelin feature... If population rises my limit, the skills become less useful. Usually my gameplan was to capture colonies, then give em to Independents, cause they always friendly anyway.