  We demonstrate the robustness of the recently established Floquet-assisted
superradiant phase of the parametrically driven dissipative Dicke model,
inspired by light-induced dynamics in graphene. In particular, we show the
robustness of this state against key imperfections and argue for the
feasibility of utilizing it for laser operation. We consider the effect of a
finite linewidth of the driving field, modelled via phase diffusion. We find
that the linewidth of the light field in the cavity narrows drastically across
the FSP transition, reminiscent of a line narrowing at the laser transition. We
then demonstrate that the FSP is robust against inhomogeneous broadening, while
displaying a reduction of light intensity. We show that the depleted population
inversion of near-resonant Floquet states leads to hole burning in the
inhomogeneously broadened Floquet spectra. Finally, we show that the FSP is
robust against dissipation processes, with coefficients up to values that are
experimentally available. We conclude that the FSP presents a robust mechanism
that is capable of realistic laser operation.
