Right, we could homebrew a solution to a problem we are creating, but we don't have to homebrew our way around things when we're discussing how we can make the system work better in the first place. And I think we should try to design so that there's less constraints on combinations of choices. Choosing a class shouldn't narrow race and lead to a domino effect which narrows culture which in turn narrows background. That kind of system leads to a bunch of hidden complexity that only serves to hurt abnormal builds.
I don't think linking an ASI to culture implies anything we can't imply with a better, more interesting feature. It's just locking a +1 bonus behind a door labeled "illusion of choice". Linking a Roleplay talent or feature akin to the Folk Hero's Rustic Hospitality or the Charlatan's False Identity encourages people to interact more with their culture in a way that is interesting and encourages the kinds of play I think we both want to see at the table without basically winding up with the problem of race/class combos but with one of the words swapped out.