"Too strong" is subjective, but you'll run into a bunch of issues
1. It can now be influenced by Metamagic
A Dragonborn sorcerer could use Metamagic to increase range, use "Careful" to breath around a team mate, you "Subtle" to make it somehow hidden, "Quicken" to make it a bonus action attack, and "Transmuted" to change the damage type.
2. You're now a "spellcaster" as far as feats are concerned
Since the character's breath is a spell, they now qualify for any feat that has a prerequisite of being a spellcaster. This won't be useful to most feats, but the Elemental Adept feat states:
When you gain this feat, choose one of the following damage types: acid, cold, fire, lightning, or thunder.
Spells you cast ignore resistance to damage of the chosen type. In addition, when you roll damage for a spell you cast that deals damage of that type, you can treat any 1 on a damage die as a 2.
This means that all of their breath weapons deal more damage and can be used even if the creature they are fighting is normally resistant to the character's attack.
3. On the flip side, the breath weapon can be "countered"
As a spell, and most likely visible, an enemy caster can counterspell the breath. It has no spell level so it would likely be treated as a cantrip and would always be countered by the 3rd level counterspell.
Similarly, it would be subject to anti-magic spells and zones, as well as certain creature's "magic immunity" like the rakshasa.
4. It has no school of magic
This may or may not have ramifications, but it is still important to bring up as Wizards of different subclasses can benefit or enhance spells of their assigned school. So if you declared Dragonborn breath as evocation, then it might be influenced by Sculpt Spell, Potent Cantrip, Overchannel, etc...
In the end, you're better off buffing it in other ways
While making the breath weapon a spell so that it can be influenced by magic shaping feats/skills/features may seem like a good idea, you're opening yourself up to a lot of hassles; with the right setup it becomes OP.
A better option would be to make it level up like a cantrip. At certain character levels, the damage and DC increase to keep it useful throughout the life of the character.