  Recent advances in generating well controlled dense arrangements of
individual atoms in free space have generated interest in understanding how the
extended nature of these systems influences superradiance phenomena. Here, we
provide an in-depth analysis on how space-dependent light-shifts and decay
rates induced by dipole-dipole interactions modify the steady-state properties
of coherently driven arrays of quantum emitters. We characterize the
steady-state phase diagram, with particular focus on the radiative properties
in the steady-state. Interestingly, we find that diverging from the
well-established Dicke paradigm of equal all-to-all interactions significantly
modifies the emission properties. In particular, the prominent quadratic
scaling of the radiated light intensity with particle number in the
steady-state -- a hallmark of steady-state Dicke superradiance -- is entirely
suppressed, resulting in only linear scaling with particle number. We show that
this breakdown of steady-state superradiance occurs due to the emergence of
additional dissipation channels that populate not only superradiant states but
also subradiant ones. The additional contribution of subradiant dark states in
the dynamics leads to a divergence in the time scales needed to achieve
steady-states. Building on this, we further show that measurements taken at
finite times for extended atom ensembles reveal properties closely mirroring
the idealized Dicke scenario.
