  We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and
\cite{LafforgueNaor14_GD} about the impossibility of dimension reduction for
doubling subsets of $\ell_q$ for $q>2$. We provide an alternative elementary
proof of this impossibility result that combines the simplicity of the
construction in \cites{BGN_SoCG14,BGN_SIAM15} with the generality of the
approach in \cite{LafforgueNaor14_GD} (except for $L_1$ targets). One advantage
of this different approach is that it can be naturally generalized to obtain
embeddability obstructions into non-positively curved spaces or asymptotically
uniformly convex Banach spaces.
