  We study the impact of quenched disorder on the dynamics of locally
constrained quantum spin chains, that describe 1D arrays of Rydberg atoms in
both frozen (Ising-type) and dressed (XY-type) regime. Performing large-scale
numerical experiments, we observe no trace of many-body localization even at
large disorder. Analyzing the role of quenched disorder terms in constrained
systems we show that they act in two, distinct and competing ways: as an
on-site disorder term for the basic excitations of the system, and as an
interaction between excitations. The two contributions are of the same order,
and as they compete (one towards localization, the other against it), one does
never enter a truly strong disorder, weak interaction limit, where many-body
localization occurs. Such a mechanism is further clarified in the case of
XY-type constrained models: there, a term which would represent a bona-fide
local quenched disorder term acting on the excitations of the clean model must
be written as a series of non-local terms in the unconstrained variables. Our
observations provide a simple picture to interpret the role of quenched
disorder that could be immediately extended to other constrained models or
quenched gauge theories.
