Do fleets have to have a commander?

Yes.

You have to have one commander in a fleet, but you can only have one. The ship the commander is assigned to is the flagship.

Page 6 of the rules reference:

"A fleet must have one flagship and cannot have more than one flagship."

"A flagship is a ship equipped with a commander card."

So eventhough the rules do not specifically state you need a commander in a round about way they do.