I do think this is a really interesting distinction between Inspiration as it is and the direction they're taking Inspiration in. Right now, DM's give Inspiration, and they give it in a kind of vague and nebulous way, like a little cookie for "good RP" whatever that is. And then it's easy to forget or not use because who KNOWS when that'll happen again. It definitely doesn't feel like something I control, as a player.I think that is the rub, some groups do this naturally, and others need system assistance. The vague triggers can be arbitrary and seen as "mother may I" type play. I like the inspiration on 20 roll because its a rare, but tangible trigger. I also like getting inspiration on a 1 roll too.
Giving the players a more active hand in generating inspiration is a great idea.
I think what I don't like is linking it to builds or to luck. The thing I want players to do is not to fish for 20's to get 1/day advantage. I want them to engage with their characters and the world. I don't want to replace bardic inspiration with Inspiration.
I am more OK with them spending Inspiration being part of builds or a way to tweak luck. Give Bards a unique way to spend Inspiration on their allies.
But keep Bards earning Inspiration by leaning into their character flaws and world elements.
Like, maybe Bards have a class feature called True Artist and if the bard creates a new composition in the world, they get Inspiration. And then maybe they can spend it to gain a bonus use of Bardic Inspiration. I would like my bard characters to make songs. That is DOPE.