Is this alteration to the Evocation Wizard's Potent Cantrip balanced?

Question

The Potent Cantrip ability states:

Starting at 6th level, your damaging cantrips affect even creatures that avoid the brunt of the effect. When a creature succeeds on a saving throw against your cantrip, the creature takes half the cantrip's damage (if any) but suffers no additional effect from the cantrip.

This seems to limit the wizards choices, as there is no benefit of this feature to cantrips like Firebolt or ray of frost. My alternative proposal is this:

Starting at 6th level, you add your Intelligence modifier to the damage you deal with any wizard cantrip that does not already add an ability modifier.

There is precedent to adding an ability modifier to a cantrip, as seen in the Cleric's Potent Spellcasting or the Warlock's Agonizing Blast. The additional "...that does not already add an ability modifier" is to account for spells like Magic Stone or Booming Blade, so these cantrips would not stack modifiers. The main reason I feel this may not be balanced is that this ability is given at 6th level, as opposed to the Cleric receiving it at 8th level.

Answer 1

This probably makes the Wizard strictly worse at 10th level.

This feature is just the 10th level Evocation Wizard feature restricted only to cantrips. Empowered Evocation says:

Beginning at 10th level, you can add your Intelligence modifier to one damage roll of any wizard evocation spell you cast.

Empowered Evocation applies to your Evocation cantrips, so at 10th level, you basically don't have a 6th level subclass feature anymore, at least, it only benefits your non-Evocation cantrips (there are 8 non-Evocation wizard cantrips with the damage tag on DDB, and 8 Evocation cantrips with the Evocation tag). Unless you're planning ahead, chances are high your damaging cantrips are Evocation.

From levels 6 to 9 it is probably a little better, but not game breaking.

From 6th to 9th level, we don’t have the feature conflict we see at 10th and above. At these levels, this feature will likely be a small improvement over Potent Cantrip. As written, Potent Cantrip only helps those cantrips which utilize saving throws. Your version will boost these as well as attack roll cantrips. The boost isn’t huge, and successfully saving against a saving throw cantrip will still negate all damage, but it still makes your Arsenal a bit more diverse. It isn’t much, but I think it will work out to a small improvement. It will just get awkward at 10th level when it doesn’t really do anything.