And using it just once a day it's still a pretty amazing ability. Better, by far, than any other level 3 subclass ability. Vastly better than Action Surge (at least in terms of dpr).
Is it? Let's compare a 3rd level Fighter (Battle Master, 16 Dex, wielding 2 short swords, TWF Fighting Style) with a 3rd level Barbarian (Frenzy, 16 Str, wielding a greatsword)
Round 1 (B): The Barbarian rages and takes a single swing. 2d6+5 damage
Round 2 (B): The Barbarian takes one swing as an action, and another as a bonus action. 4d6+10 damage
Round 3 (B): The Barbarian takes two swing just like last round; let's model the impact of Reckless Attack by saying the Barbarian gets a crit here, because advantage will do that from time to time. 6d6+10 damage
Total: The DMG recommends using the first three rounds when assessing damage output, so let's end combat and take a tally here. 12d6+25 (67 average) damage
Round 1 (F): The Fighter attacks once as an action. The Fighter attacks again with an Action Surge! The Fighter attacks a third time with their off-hand weapon as a bonus action. He decides to spend superiority dice on all of these attacks. 3d6+3d8+9 damage
Round 2 (F): The Fighter attacks once as an action, and again as a bonus action; he has one superiority die left, and spends it on his first attack. 2d6+1d8+6 damage
Round 3 (F): The Fighter attacks once as an action. Healing is as good as damage, so the Fighter decides to pop his Second Wind as a bonus action. 1d6+1d10+6 damage (including healing)
Total: Like with the Barb, we'll stop at round 3. 6d6+4d8+1d10+21 (65.5 average) damage
These damage numbers look pretty even, despite the Barbarian burning through a long rest worth of resources while the Fighter burns through only a short rest's worth. Let's say the maneuver the Fighter was using was Precision Strike because otherwise, by assuming all attacks are hits, we aren't being fair to the accuracy the Barbarian gains from Reckless Attacks, even with that crit I threw in there.
Imagine if the Wizard class had, "After you've used all your spell slots for the day* you can still keep using your highest level spells, but you'll get a level of exhaustion each time." Wouldn't that be a $%$^ing incredible card up their sleeves?
More like: imagine if Wizards had to get a level of exhaustion each time they expend a spell slot above 2nd level to cast a spell. You have to expend rage uses just like the Wizard expends spell slots, and unlike the Wizard feature you pitched you are not gaining exhaustion to
keep using frenzy, you are gaining exhaustion to use frenzy
at all.
What's more gimped: a wizard without any spell slots, or a barbarian with one level of exhaustion?
I'm glad you brought this up, because it is another thing that bothers me. The Barbarian with exhaustion has disadvantage on ability checks, reducing their ability to contribute to the exploration and social pillars of the game where I've always believed casters already have a bit of an unfair advantage to begin with. A Wizard without spell slots still has their cantrips and rituals.