In practice a 14th level bard is not missing with 7 attack cantrips a day.
You have enough spell slots you may not even need to use a cantrip, and half the time you will hit.
It doesn't matter if it's attack cantrips or attack spells that might be used instead.
Using cantrips, like using skill checks, has the added benefit of saving slots for prepared spells for other uses. Now that bards have better attack cantrips those cantrips can be leveraged that way more.
Per day isn't a relevant marker here. It's uses over time. For every X number spent in that way Y results have occurred.
Per day requires 15-20 attacks being used this way which is only depends on how the player is choosing to use those actions in combat and to use those spell slots in other ways outside of combat.
Lore bard abilities create flexibility in how the PC uses actions effectively in and out of combat.
Also, not using a BI when you fail a climb check and fall into lava is not exactly a prize. Sure you can spam it on low risk diplomacy checks to flirt with every guy in town. Never said it couldn't be fun.
Fun is the point of playing.
I would use these abilities when they matter. That was an assumption of throwing BI dice away when they don't matter, which isn't a useful assumption.
Weird take, but in doing so the fact that every failed Peerless Skill use that fails is still adding up replacement BI dice compared to every BI spammed on fun under the same assumption that continue to be lost hasn't changed.
Mass spamming under your scenario increases the rate per day or rate per rest as Superior Inspiration comes into play or by low level spell slot spell slot supplement.
The only thing spamming does is increase the rate at which replacement BI is generated.