I also think that frenzying should not be an action, allowing the extra attack on the turn you start it.
Frenzy itself isn't an action or bonus action. Going into Rage is a bonus action and making it a Frenzy is part of the same bonus action. Since you already used your bonus action to start a rage you can't use it to attack. But I get what you are saying, going into a rage should be a free action, just like action surge for fighters.
What do you think? Should rage ignore exhaustion while you are raging? It would sure make the Path of the Berserker a little bit more viable...