Photoinduced phase separation in mixed halide perovskites emerges from their electro-mechanical properties and high ionic conductivities, resulting in photoinduced I--rich charge carrier traps that diminish photovoltaic performance. Whether photoinduced phase separation stems from the polycrystalline microstructure or is an intrinsic material property has been an open question. We investigate the nanoscale photoinduced behavior of single-crystal mixed Br-/I- methylammonium (MA+) lead halide perovskite (MAPb(Br xI1- x)3) nanoplates, eliminating effects from extended structural defects. Even in these nanoplates, we find that phase separation occurs, resulting in I--rich clusters that are nucleated stochastically and stabilized by polarons. Upon lowering the electron-phonon coupling strength by partially exchanging MA+ for Cs+, a phase-separated steady state is not reached, nevertheless transient I- clustering still occurs. Our results, supported by multiscale modeling, demonstrate that photoinduced phase separation is an intrinsic property of mixed halide perovskites, the extent and dynamics of which depends on the electron-phonon coupling strength.