Intriguing about the incarnation of the local deity being identified with the specific geographical region. In one sense, the same could be said of the biblical God and the Tabernacle of the Israelites; Yahweh wasn’t originally tied to a geographical region, but was the deity of a nomadic people. Eventually, once those nomads invaded Canaan and settled down, taking the land as their own, Yahweh, with the Temple Solomon constructed in Jerusalem, morphed into a local deity … who eventually was promoted to the top dog (alpha male god?) of all creation.
One major difference between the god of the Israelites and those of your local temples is that the Holy of Holies was veiled – not only was the High Priest the only individual allowed to enter, but the inner sanctum was walled off from view by a heavy veil. Correct me if I’m wrong, but that doesn’t appear to be the case with the garba griha – though they can’t enter the room that holds the divine presence, seems adherents are able to peer into the garba griha.