Answering this question might require looking at a very big picture.

If I remember accurately, and infer corrrectly:

Defeating a primal causes its aetherial form to shatter; it rapidly dissolves back into mist and returns to the Land (or, more vaguely, to the natural order). One who has defeated a primal has themselves necessarily been bathed in this aetherial dispersion, and is forever host to a trace of its essence. Egi, therefore, appear to be summoned, at least in part, from within. The "big six" primals we've met so far were deiformed essences of the Land itself - the six elements. The elemental wheel being what it is, each element is an imbalanced facet of aether as a whole and is strong or weak against some of its counterparts. The reason for going to a location where the element is dominant is to shift the summoner's aetherial aspect towards that element, making it easier for them to shape and project that avatar.

In the hypothetical case that the summoner was going to summon the egi of an unaspected primal, the elemental balance might not matter at all (or, inverse to the aspected primals, might work better in places that have balanced aetherial concentrations). The easiest and most logical thing would be for SE to just hold the Austerities near where the primal actually appeared and let the why happen organically. For example, a hypothetical Moggle-Egi Austerity might be held at the Bramble Patch.

It's probably all moot, though, since I assume that by the time SE offers us egi beyond the big six, the whole subject of primals will be more fleshed out and it'll be easier to justify when they start throwing whatever in there.