While polarons, charges bound to a lattice deformation induced by electron-phonon coupling, are primary photoexcitations in bulk metal-halide hybrid organic-inorganic perovskites (HOIPs), excitons, Coulomb-bound electron-hole pairs, are the stable quasi-particles in their two-dimensional (2D) analogues. However, are polaronic effects consequential for excitons in 2D-HOIPs? We argue that they are manifested intrinsically in the exciton spectral structure, which is composed of multiple nondegenerate resonances with constant interpeak energy spacing. We highlight population and dephasing dynamics that point to the apparently deterministic role of polaronic effects. We contend that an interplay of long-range and short-range exciton-lattice couplings gives rise to exciton polarons, which fundamentally establishes their effective mass and radius and, consequently, their quantum dynamics. Finally, we highlight opportunities for the community to develop the rigorous description of exciton polarons in 2D-HOIPs to advance their fundamental understanding as model systems for condensed-phase materials with strong lattice-mediated correlations.