Is this house rule to balance the college of whispers bard balanced?

As a player and a dungeon master, I feel like the Psychic Blade of the college of whispers bard is really unbalanced regarding the Sneak Attack feature of the rogue.

First of all, they mostly does the same amount of damage… But the Psychic Blade does psychic damages, where the sneak attack’s damage type is the one of the weapon (bludgeoning, piercing or slashing). The problem is that psychic damage is one of the less resisted type of damage, where bludgeoning, piercing and slashing damages are the most resisted type of damages.

Second, Psychic Blade is way easier to trigger than Sneak Attack, only needing to spend a Bardic Inspiration (which come back on short rest after level 5) and you have it, where Sneak Attack require advantage or an ally to use it.

So, looking those elements, I decided to replace the cost Bardic Inspiration of Psychic Blade with a condition. To use the Psychic Blade feature, you don’t need to spend a Bardic Inspiration, you need advantage on charisma check against your target, be under the Mantle of Whispers feature effect, or the target have to be frightened or charmed before the attack hit.

To me, it keep the flavor of a bard that is also a killer, still synergyse with the others college of whisper features, but make it a little bit harder to the bard to have the Psychic Blade. But is it balanced?