  We describe a homotopy-theoretic approach to the theory of moduli of
realizations of Blanc-Dwyer-Goerss, reproducing their obstructions to realizing
a given $\Pi$-algebra as homotopy groups of a pointed space. Our techniques are
based on the $\infty$-category $\mathcal{P}_{\Sigma}(\mathcal{S}ph)$ of
product-preserving presheaves on finite wedges of positive-dimensional spheres,
leading to more conceptual and streamlined arguments.
