Sure.
But one rule I like is "dice are fun".
I would start by giving the class a Prodigy die, d4 to start and scale up.
Then tie features to it. Damage, skill bonuses, save bonuses, etc.
It also becomes a physical token of the class's specialness. And you can hang other mechanics on it.
As a small side bonus, it makes the class slightly more MC friendly, as it scales with class levels.
As this class is intentionally simple, this one tiny mechanic isn't overwealming it with complexity. You just get more stuff to use it on as you gain levels.
Categories can include:
- Damage
- Attack rolls
- Skill checks
- Initiative
- Saves
- AC/Prevent damage
- Death saves
- Aid allies at above (expend reaction maybe)
If die scales d4 to d12 similar to proficiency, bonus is similar but less reliable.
And then carry it forward: At L11, instead of extra attacks (and stealing Fighter's thunder), add Prodigy die to attack and damage rolls. Impact is similar.