I wouldn't want Bardic Inspiration to be a prompt because it could activate multiple times per turn, and then even more times per round. Same reason I don't want Smite to be a prompt, basically.
Would it, though? From what I am reading Bard has to choose his target, the same way as it is already in EA. So really, prompts will only pop up if said character is being attacked - I don't think that would be excessive outside occasional fringe situatations. On top of that, Inspirations are limited resource, so I imagine vast majority if players will cast the Inspiration (instead of, for example, pushing someone to death) if there is particular enemy they are worried about.
Solasta should be adding Bard through a DLC sometime in the future, so I am curious to how it will play there.
It sounds like you're confusing Bardic Inspiration ("players will cast the Inspiration") and Cutting Words (you refer to "if said character is being attacked"). With Cutting Words, the bard can subtract a Inspiration die from any incoming attack or damage roll. So yes, with a Prompt implementation a Bard would be prompted every single time an enemy attacks an ally, twice--once for the attack and once for damage--until they run out of Inspiration. I agree with Larian's choice to make Cutting Words in BG3 an activated ability that subtracts the BI die from all enemy rolls for a turn.
For Bardic Inspiration, the bard casts it on an ally with a bonus action. Then, RAW, that ally can choose to use that die anytime in the next 10 minutes, and apply it to any one ability check, attack roll, or saving throw. In BG3, "10 minutes duration" would likely change to "until next rest," and at level 5 Bardic Inspiration recharges on a short rest, so I'd expect ~all players to have Bardic Inspiration at all times since the Bard would cast it out of combat. Thus, almost every time a player makes a roll they'd be prompted to use the inspiration, until they use it up.
Similar to Cutting Words, I'd suggest that Bardic Inspiration buffs ALL of an ally's rolls for 1 round. Both implementations trade the power of saving the inspiration for an important roll in exchange for being slightly more powerful in *all* rolls for 1 turn. Alternatively, Bardic Inspiration could last forever but be used automatically on the next Attack roll/Saving throw where using it could change the outcome.
I am also curious about how Solasta will implement the Bard.