Your suggestion to have some of the class specific options be shared with classes is interesting, but I am not in favour of it.
First of all, BG3 already homogenised classes too much for my taste - having class specific options be available to other classes is not something I like the sound of. More importantly, I think such change would encourage unintuitive meta gaming. I surely, with a system like that you would never want a bard with entertainer background, as you wouldn’t gain much benefit from it. At the same time, picking a background not fitting your class (to maximise the benefit) would reward choices not to the class’s strength through inspiration system.
You do have a point there.
Except I don't believe that " background not fitting your class " is a thing. There's always ways to create unique characters that way 😛
The issue would be "background not fitting you character" in my opinion.
But for the rest, yes. I agree actually.
Connecting class specific and background specific sounds interesting for single playthrough ...
But would negatively affect replayability im affraid.

I'm not sure how that's true and I will never be in favor of removing options just to force replay-value. Especially when it means "forcing" players to pick either vanilla answers (usually black or white) or one specific stereotype related to a class.
But I may see your point and
yes the first solution given might not be ideal either.
For example, adding "witty"/"funny" answers (currently mostly locked behind the Bard class) to a specific Background is not really an solution.
Many people picking different class might want those options without picking that one specific background.
But here's why it's a shame that Background don't receive more love and that "stereotypes" are locked behind classes :Currently, the game seems to rely on one stereotype per class.
So, excluding "vanilla" options (to make things easier, I don't believe it would impact that much anyway), they can only be 12 "uniques" stereotypes (the 12 classes from the PHB).
However, if Backgrounds are given a little more love (meaning new tag options), we could have 156 unique combinations between Background and Classes.
(If the 12 classes and 13 backgrounds are released : 12 x 13 = 156).
Also, Backgrounds are supposed to give access to certain items and other proficiencies that aren't in the game at all.
For example, Entertainers should be able to play an instrument according to PHB. Criminals should have proficiency with thieve's tools.
With how things currently works and how Backgrounds don't add anything meaningful in terms of RP or gameplay :
- Custom characters won't have much opportunities to have depth
- People would be invited to pick Backgrounds only for the skill proficiencies. The inspiration points system is not that thrilling or impactful anyway.
Also i remember Swen talking in some interview that Backgrounds will not be used as dialogue choices, bcs there would be too much permutations for them to handle. :-/
Wich is understandable ... adding another symbols makes total amount of permutations grow exponencialy. :-/
Easy solution then, and one they already know about :
adding different options (to had flavor) resulting in the same output. I would settle for that. Better that than no love for Backgrounds.
But hey, all things come to worst...I'll be disappointed and then I'll multiclass my Tav as a Bard/Paladin (Lore/Ancients). No regret. The spreadsheet has already been made 😄. The Backgrounds would still be meaningless but I'll get to play the character as I want (well...more or less).
Note: that post probably sounds more ranty that intended 😅 Oh well 😆 There are days like this. I guess I'm feeling extra passionate about the issue today 😅