Should a soldier be switched units upon promotion to E-5?

Absolutely not. You'll be dealing with your peers being placed above you, or being placed over your peers, your whole life. There's no reason to try to pretend it's not an issue by avoiding the conflict. The sooner a new NCO can overcome that first obstacle their authority, the sooner they can grow as a leader. It's better to face that early in your career and understand how to deal with it than it is to face it for the first time as a senior NCO and not know how to navigate that thorny issue. As you get promoted higher and higher, the promotions slow down and suddenly you're all the same rank with people who out ranked you years ago, and people you out ranked as well. You'll be placed on projects where one of you is in charge of the others and you have to know how to lead them

Yes. Change in one's unit is typically imminent anyway. Moving a newly promoted SGT to a new unit can help with your initial start as a leader because your peer group is no longer mix matched with friends who are still junior enlisted. It also helps to establish an environment of more solid respect because your soldiers will have now only known you as a SGT. Embrace the change because it's going to happen regardless.

IMO, yes. The pull of the E-4 mafia and "Good buddies" may cause issues with you doing your new job as a NCO.