This is true in many legislations, actually (unbeknownst to many cyclists).

I'd tag it as just highway=cycleway and leave out foot completely: if it is missing, it means that the defaults apply. In case of Georgia, that would be that pedestrians are allowed, as you write. An explicit tag implies (somewhat) that there is a sign.

(In Germany, for example, there IS a sign for foot=yes and not designated)