thanks w2aew you've reinforced my understanding. its just because of "natural selection" that hasnt "evolved", we just follow the trandition (industries)
such confusion is demonstrated in the OP, thats why i brought this thing up. but anyway, i understand why we cant get rid of the term "ground" (0V), its our ultimate reference anyway (earth).
back to OP, the C1 is to pass AC signal component and blocking DC component, hence the signal out of C1 will be pure AC (centered at 0V), the R1 and R2 voltage divider is just to provide another DC biasing for the AC signal so it will be centered at opamp's midpoint, ie Vs and 0V. that is for "single" supply circuit which i believe the OP copied from 100% in the first place. since the OP are now using "split symetric" supply, there is no more need for the AC coupler + bias network, unless your input signal common mode (DC component) is way off, then you'll need to put the C1 to block the common mode voltage (i hope i used the term "common mode" correctly).
I agree completely with your logic here but again, semantically, your "typical" split supply configured op-amp has 3 nodes +ve, 0V and -ve, typically sahred throught the entire system where as the single has only 2 and you have to create the 3rd and normally isolate it from the rest of the circuit usually via ac coupling
from my understanding, the 0V reference is not for the opamp, but for the whole circuit. but anyway i cant disagree, you look at it from different perspective, which is how normally the way people think of (including me most most most of the time).