Is this "School of the Wyrm" wizard subclass I found balanced?

Question

I found this wizard subclass in [this document] on DMsGuild, and I'd like to know if it is balanced compared to the existing classes .

School of the Wyrm

Knowledge of the Wyrm

Beginning at 2nd level, you gain proficiency with the Arcana skill, and you can speak, read, and write Draconic. Your proficiency bonus is doubled for any ability check you make that uses Intelligence (Arcana).

Additionally, whenever you make a Charisma check while interacting with dragons, your proficiency bonus is doubled if it applies to the check.

Spell Research

Choose one of the following classes: Bard, Cleric, Druid, or Warlock.

Starting at 2nd level, you can learn spells from the chosen class's spell list. The spell must be of a level for which you have spell slots.

Any spell you gain from this feature is considered a wizard spell for you, but other wizards can’t copy non-wizard spells from your spellbook into their own spellbook.

Draconic Discovery

Starting at 6th level, you gain a number of sorcery points equal to your Intelligence modifier. You regain all spent sorcery points when you finish a long rest.

You also gain the ability to twist your spells to suit your needs. You gain one of the Metamagic options of your choice from the sorcerer's Metamagic class feature. You gain another one at 12th (two) and 18th level (three).

You can use only one Metamagic option on a spell when you cast it, unless otherwise noted. When you use a Metamagic option, you can use your Intelligence modifier instead of your Charisma modifier.

Convert Counterspell

Beginning at 10th level, when you see a creature casting a spell within 60 feet of you, you can use your reaction to try to magically foil it. The creature must succeed on a Wisdom saving throw against your spell save DC, or its spell fails and you regain one sorcery point.

You may use this ability a number of times equal to your Intelligence modifier (a minimum of once). You regain all expended uses when you finish a long rest.

Draconic Arcanum

At 14th level, you gain the ability to empower your spellcasting with draconic magic. As an action, you undergo a transformation, causing arcane energy to radiate from within you, pouring out of your eyes and mouth. For 10 minutes, you gain the following benefits:

• Creatures cannot gain advantage on saving throws to resist spells you cast.
• You shed bright light in a 10-foot radius and dim light for an additional 10 feet.
• Once on each of your turns, you can deal extra force damage to one target when you deal damage to it with an attack or a spell. The extra force damage equals your Intelligence modifier.

Once you use this feature, you can't use it again until you finish a long rest.

My musings:

I imagine this subclass as a wizard learning from a dragon and said dragon's hoard of magic books.

I worry that this might be stepping on other classes' toes too much:

• Spell Research allows the wizard to take spells from other classes, but seems like it might be balanced, as it requires access to spells to copy. Answers to this question should note whether it would be too OP to allow spells from the chosen class to be taken on a level-up.
• Draconic Discovery allows usage of one of the sorcerer's primary features. Note however that sorcerer cannot be chosen for Spell Research, limiting the mimicry slightly.
• Draconic Arcanum is somewhat like paladin subclass capstones. I think it is probably different enough, though.

Answer 1

This is unbalanced and badly designed

The second level feature of this gives you the option to cast any spell from a cleric or druid spell list. There's no need to look at any of the other features: this in itself is undermining the class balance in such a fundamental way that this subclass is unbalanced.

The selection of spells you have access to is one of the defining features of spellcasting classes. There are ways this may be softened in very limited ways (like the Bards ability to learn a handful of spells of other classes, which is one of its strongest features, or the cleric's domain spell which can in some cases give them access to non-cleric spells). But there is no precedent of giving wizards with their already large spell selection access to all spells of another class in that way, for a reason: its against the game's design to make the classes distinct.

The DMG even advises against this explicitly, on page 283:

Make sure the spell fits with the identity of the class. Wizards and sorcerers don't typically have access to healing spells, for example, and adding a healing spell to the wizard class list would step on the cleric's turf .

This is not adding a healing spell, it is adding all of them , along with raising the dead and all the other things that are the domain of divine casters.

The sixth level feature then goes on to give you metamagic and as many sorcery points as a sorcerer has. These are the main defining features of yet another class, and to balance having them, sorcerers have a much narrower selection of spells known, not the huge wizard list with the ability to prepare any. This also, just by itself would be broken, and in combination with gaining all spells from the cleric lists is utterly ridiculous.

Maybe, when looking at these homebrew subclasses, ask yourself: does this look too good to be true? If it does, it probably is.

Answer 2

No, it is overpowered, and as as you've noticed, steps on the toes of others classes

I see the following problems with it:

Spell Research negates the most significant limitation of the Wizard - despite the huge amount of spells available to them, they do no have access to healing magic and getting access to it should come at a significant cost, like a Cleric dip. This subclass can grab all the healing spells that a Cleric has access to. This alone is enough to make this badly designed.

Draconic Discovery - expands the subclass too much into Sorcerer's territory. Metamagic is the defining Sorcerer's feature, that you usually have to either multiclass or take a feat to access and this features takes away from that. The progression of Metamagic options is too close to that of the Sorcerer's (you just get 1 initially instead of 2 and then gain 2 more just like the Sorcerer, just a level or two later). It also allows a very generous amount of sorcery points.

Convert Counterspell - Counterspell for free without having to learn it, usable 5 times per long rest (by this level any Wizard will almost certainly have Intelligence of 20 and that's assuming without any increases apart from ASIs), without expending a spell slot. That's more times than you get spells slots of spell level 3 (which Counterspell is). This is ridiculously powerful just on it own, to make things worse, a successful use restores a sorcery point, potentially giving you 10 sorcery points' worth - as many as a Sorcerer has at this level.

Answer 3

As you said, it definitely steps on the toes of other classes (giving that it allows the wizard to cast any spell from the Cleric or Druid spell) as well as giving them metamagic which is the Sorcerer's main feature (and the two classes already share a lot of the same spells).

Even ignoring that, a counterspell FOR FREE is really strong in most campaigns which is further unbalanced by the number of uses it has. If it was once per long rest it'd still be good but I think it would be fine, but being able to use 5 (I'd assume by the time you get that feature you would have a maxed Intelligence score) per long rest is too often and spammable.