Is this homebrew Circle of the Bloodlust Druid subclass, which replaces Wild Shape with a Berserker barbarian's Frenzied Rage, balanced?

Question

Would it be balanced to replace the Wild Shape feature of a druid with Rage?

This homebrew is intended for a pacifist supporting spellcaster, cursed with a violent blood lust curse. This homebrew is intended to capture the feeling of the character loosing his temper(ranging from someone harassing him in a bar, to witnessing his friend knocked unconscious by an enemy), going berserk and after words dealing with the regret and self disgust caused by the violence. The character is intended to be effective in a fight while in a rage, but generally a more valuable resource while calm to provide incentive for the rest of the party to keep him calm.

Circle of the Bloodlust (tentative name)

Rage would function as it does for a barbarian but without access to Reckless Attack, Relentless Rage, and Persistent Rage. He could rage 2 times per short rest for the 2 Wild Shapes per short rest. Additionally he would only go into frenzied rages (from the Berserker subclass) by taking a point of exhaustion to represent the disgust at injuring a creature. Below are the Barbarian features he would have:

Rage

In battle, you fight with primal ferocity. On your turn, you can enter a rage as a bonus action.

While raging, you gain the following benefits if you aren’t wearing heavy armor:

• You have advantage on Strength checks and Strength saving throws.
• When you make a melee weapon attack using Strength, you gain a bonus to the damage roll that increases as you gain levels as a barbarian, as shown in the Rage Damage column of the Barbarian table.
• You have resistance to bludgeoning, piercing, and slashing damage.

If you are able to cast spells, you can’t cast them or concentrate on them while raging.

Your rage lasts for 1 minute. It ends early if you are knocked unconscious or if your turn ends and you haven’t attacked a hostile creature since your last turn or taken damage since then. You can also end your rage on your turn as a bonus action.

Once you have raged the number of times shown for your barbarian level in the Rages column of the Barbarian table, you must finish a long rest before you can rage again.

The subclass features are those of the Berserker subclass, with the exception of gaining the Berserker's 3rd level feature at 2nd level;

Frenzy

Starting when you choose this path at 2nd level, you can go into a frenzy when you rage. If you do so, for the duration of your rage you can make a single melee weapon attack as a bonus action on each of your turns after this one. When your rage ends, you suffer one level of exhaustion.

Mindless Rage

Beginning at 6th level, you can’t be charmed or frightened while raging. If you are charmed or frightened when you enter your rage, the effect is suspended for the duration of the rage.

Intimidating Presence

Beginning at 10th level, you can use your action to frighten someone with your menacing presence. When you do so, choose one creature that you can see within 30 feet of you. If the creature can see or hear you, it must succeed on a Wisdom saving throw (DC equal to 8 + your proficiency bonus + your Charisma modifier) or be frightened of you until the end of your next turn. On subsequent turns, you can use your action to extend the duration of this effect on the frightened creature until the end of your next turn. This effect ends if the creature ends its turn out of line of sight or more than 60 feet away from you.

If the creature succeeds on its saving throw, you can’t use this feature on that creature again for 24 hours.

Retaliation

Starting at 14th level, when you take damage from a creature that is within 5 feet of you, you can use your reaction to make a melee weapon attack against that creature.

These are features from the the Druid class that interact with Wild Shape. For now, they'll simply replace Wild Shape with Rage with some tentative tweaks . I'm a bit conflicted on these ones so please give feedback.

Beast Spells

Beginning at 18th level, you can cast some of your druid spells while raging. To cast a spell while raging, you must make a concentration check with a DC of 10. If the initial concentration check fails, the spell fails, not consuming a spell slot. In addition, you are unable to provide material components for spells while raging, limiting you to spells with only verbal or somatic components.

If the spell requires concentration, you must make a concentration check at the beginning of your turn.

Archdruid (name needs tweaking)

At 20th level, you can rage an unlimited amount of times per long rest.

Answer 1

No

First a note on the purpose of balance: the reason why it is important that player character options be balanced against each other, is so no one player can steal the spotlight. If one player plays a class that is objectively better at many aspects, including "niche" aspects of other player characters, you risk discontent among the other players. I'd feel betrayed by the DM if he'd just let me play a Berserker Barbarian, while also just giving most of my cool features to the Druid player, on top of all the stuff Druids get anyway.

This option is too weak. Even using it only once per day comes with the heavy penalty of a level of Exhaustion. Replacing Wild Shape with Rage takes away an integral part of the Druid class. It also steps on the Barbarian class' toes way too much.

The good part

I like subclasses that take a central feature of the class and open up all new ways to use it; allowing Wild Shape uses to be spent in a new way is a cool, flavorful, new option.

Power-wise, a Frenzied Rage is not really that different from a Circle of the Moon Druid's Wild Shape; you get better at soaking up damage, gain improved melee combat capabilities, and you still can't cast spells while it is active. Even more so, if you know your player and they mostly want to do this for flavor and are not planning to optimize for it, you have less problems.

The overpowered

This subclass basically gives one class (Druid) access to the defining feature of another class (the Barbarian's Rage). There are plenty of examples throughout PHB, Xanathar and Unearthed Arcana of this, but let's look at two of the most basic ones, the Eldritch Knight Fighter and the Arcane Trickster Rogue. Fighter and Rogue - the most archetypical martial, i.e. non-caster, classes - get access to spellcasting. Closer inspection and attentive reading of the multiclassing rules shows, however, that they progress only at a third of the rate at which full caster classes do. Instead of every two levels, they get access to higher level spell slots every six levels. This is a pretty good argument that subclass-based access to another class' defining feature should only progress at a rate of 1/3. One could argue that the Rage feature progresses by means of:

1. Number of Rages per long rest
2. Rage damage
3. The Feral Instinct feature
4. The Persistent Rage feature

The first point, however, brings a couple of big problems: Barbarians start out with two rages per long rest. Coupling Rage to Wild Shape gives the Druid up to 6 Rages per day with two short rests, which is fairly realistic. (As a point of reference, in the game where I played a barbarian, I still occasionally had days where 4 Rages were not enough. This happened especially in densely packed dungeon crawls.) This means your subclass can keep raging more persistently than a Barbarian. Additionally, at level 20 a Druid gains unlimited Rages, which is also kind of part of the Barbarian capstone.

A solution for this could be to introduce a table - similar to the Eldritch Knight Spellcasting table - where you list the maximum number of Rages per long rest and the Rage Damage for every level. You would then start out with 2 rages per long rest and only raise it to 3 at level 9, and 4 at level 18. Raging would still cost you a use of Wild Shape, but you could only do so a number of times per day as specified in the table. The Rage Damage would stay at +2 for all 20 levels.

The underpowered

If I am reading your question correctly, you intend to replace the Wild Shape feature with Rage. This brings two problems. First, Wild Shape is such an integral part of the Druid, arguably the defining feature of the 5e Druid. You take that away, who says your player even wants to play a Druid anymore?

Second, by only allowing the Druid to enter a Frenzied Rage, you massively limit the usefulness of it all. Taking even a single level of Exhaustion gives you disadvantage on all skill checks! Let me tell you, from experience as a Path of the Berserker Barbarian, that sucks! It practically limits the Druid to one Rage per day, and still comes with a heavy penalty.