The slow rate of exhaustion recovery will likely restrict you to one Frenzy per day.
You relieve one level of exhaustion per long rest.
That’s right yo ur core subclass ability will kill you if you use it too much. More than one level of exhaustion is utterly debilitating for a class that relies so heavily on melee combat, and six levels of exhaustion will kill you. The cost of these bonus action attacks is exceptionally high. You may get a couple of bonus action attacks per fight. While the bonus action attack is one of the most substantial options available, you don’t get to use your bonus action attack on the first round of combat because you have to use that bonus action to enter your Rage. Your Rage is even more intense, and you make an extra weapon attack as a bonus action on your turn, after which you gain a level of exhaustion.
Frenzy – 3rd Level – Berserker Barbarian Feature