I still think inspiration would work well with pop ups. I just feel that if someone cast inspiration, they have in mind a use for it rather then just keep it for foreseeable future.
While I disagree with this reasoning (in my tabletop experience, bards don't usually give out inspiration for a specific reason in combat. This will only be more true in BG3 with the ease of long resting = replenishing of resources), I actually am coming around to BI being an okay prompt.
In my tabletop experience, players usually just use the BI die on the first applicable roll, when using it could turn a miss/fail into a hit/success. Maaaybe the 2nd applicable roll if the first use is incredibly weak: e.g., a ST against a cantrip. That'd only be 1 or 2 pop-ups in BG3, which isn't bad at all.