I can totally say that the vi chord could not work as a tonic, feeling deceptive and so on and I'm wondering why. Could it be that a chord sounds "tonic" only if it is the tonic, namely C-E-G. So also any inversion of the tonic chord won't have a tonic function. Or we can maybe better say that there are several shades of tonicity (or of finality), where we could give the
I->100%,
Ib -> 70%,
Ic -> 40%
and vib 20%, since it is still super-dominant (say, 70%) and a still sub-dominant (10%). Clearly here numbers are not the result of a deep inquire, I'm just trying to use a rough example to explain a possibly silly concept =D
As for the second part of my question, for example, the iib chord acts as a sub-dominant and the vii°b chord as a dominant, but then why can't a iiib chord act as a dominant and why is it not (usually, as far as I know, which is not so much) used in that fashion?
[Here by b and c I mean the secondfirst and the thirdsecond inversion of the chord]