Note that a 1-topos is not exactly a particular sort of 2-topos or $\infty$-topos, just as a Heyting algebra is not a particular sort of 1-topos. The (1,2)-category of locales (i.e. (0,1)-topoi) embeds fully in the 2-category of Grothendieck 1-topoi by taking sheaves, but a locale is not identical to its topos of sheaves (and in fact no nontrivial 1-topos can be a poset), in that the following diagram of functors can not be filled by a natural isomorphism:

Likewise, one expects every Grothendieck 1-topos to give rise to a 2-topos or $\infty$-topos of stacks, hopefully producing a full embedding of some sort.