  We investigate the `local consistency implies global consistency' principle
of strict width among structures within the scope of the Bodirsky-Pinsker
dichotomy conjecture for infinite-domain Constraint Satisfaction Problems
(CSPs). Our main result implies that for certain CSP templates within the scope
of that conjecture, having bounded strict width has a concrete consequence on
the expressive power of the template called implicational simplicity. This in
turn yields an explicit bound on the relational width of the CSP, i.e., the
amount of local consistency needed to ensure the satisfiability of any
instance. Our result applies to first-order expansions of any homogeneous
$k$-uniform hypergraph, but more generally to any CSP template under the
assumption of finite duality and general abstract conditions mainly on its
automorphism group. In particular, it overcomes the restriction to binary
signatures in the pioneering work of Wrona.
