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Recent observations suggest our understanding of mass loss in classical novae is incomplete, motivating a new theoretical examination of the physical processes responsible for nova mass ejection. In this paper, we perform hydrodynamical simulations of classical nova outflows using the stellar evolution code MESA. We find that, when the binary companion is neglected, white dwarfs with masses >= 0.8 Msol successfully launch radiation-pressure-driven optically thick winds that carry away most of the envelope. However, for most of the mass loss phase, these winds are accelerated at radii beyond the white dwarf's Roche radius assuming a typical cataclysmic variable donor. This means that, before a standard optically thick wind can be formed, mass loss will instead be initiated and shaped by the binary interaction. An isotropic optically thick wind is only successfully launched when the acceleration region recedes within the white dwarf's Roche radius, which occurs after most of the envelope has already been ejected. The interaction between these two modes of outflow -- a first phase of slow, binary-driven, equatorially focused mass loss encompassing most of the mass ejection and a second phase consisting of a fast, isotropic, optically thick wind -- is consistent with observations of aspherical ejecta and signatures of multiple outflow components. We also find that isolated lower-mass white dwarfs <= 0.8 Msol do not develop unbound optically thick winds at any stage, making it even more crucial to consider the effects of the binary companion on the resulting outburst.