  Single-field models of accelerated expansion with nearly flat potentials,
despite being able to provide observationally viable explanations for the
early-time cosmic inflation and the late-time cosmic acceleration, are in
strong tension with string theory evidence and the associated de Sitter
swampland constraints. It has recently been argued that in an open universe,
where the spatial curvature is negative (i.e., with $\Omega_k>0$), a new stable
fixed point arises, which may lead to viable single-field-based accelerated
expansion with an arbitrarily steep potential. Here we show, through a
dynamical systems analysis and a Bayesian statistical inference of cosmological
parameters, that the additional cosmological solutions based on the new fixed
point do not render steep-potential, single-field, accelerated expansion
observationally viable. We mainly focus on quintessence models of dark energy,
but we also argue that a similar conclusion can be drawn for cosmic inflation.
