  Symmetry-breaking instabilities play an important role in understanding the
mechanisms underlying the diversity of patterns observed in nature, such as in
Turing's reaction--diffusion theory, which connects cellular signalling and
transport with the development of growth and form. Extensive literature focuses
on the linear stability analysis of homogeneous equilibria in these systems,
culminating in a set of conditions for transport-driven instabilities that are
commonly presumed to initiate self-organisation. We demonstrate that a
selection of simple, canonical transport models with only mild multistable
non-linearities can satisfy the Turing instability conditions while also
robustly exhibiting only transient patterns. Hence, a Turing-like instability
is insufficient for the existence of a patterned state. \ak{While it is known
that linear theory can fail to predict the formation of patterns, we
demonstrate that such failures can appear robustly in systems with multiple
stable homogeneous equilibria.} Given that biological systems \ak{such as} gene
regulatory networks and spatially distributed ecosystems often exhibit a high
degree of multistability and nonlinearity, this raises important questions of
how to analyse prospective mechanisms for self-organisation.
