An example of when none elected officials is an advantage would be, appointing judges. This allows them to focus on making decisions based on law and not on what their voters about their decisions. Any branch of government that needs to make decisions on what is based on constitution, and laws need to not be publicly voted in to position (Brown, N/A).
Disadvantages of having a branch of government that is not democratically elected?
One disadvantage is the people not having a say in the type of judge that gets that position, a judge can be elected in by a president just because they are good friends, even though this person may be a terrible fit