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In the absence of environmental steering, tropical cyclone (TC) motion largely reflects "beta drift" owing to differential planetary vorticity advection by the storm's outer circulation. It is known that model physics choices (especially those relating to convection) can significantly alter these outer winds and thus the storm track. Here, semi-idealized simulations are used to explore the influence of the initialization on subsequent vortex evolution and motion. Specifically, TCs bred from a buoyant "bubble" are compared to bogussed vortices having a wide variety of parameterized shapes and sizes matching observations. As expected, the bogussed storms commencing with the strongest outer winds propagated fastest and, as a result, huge structure-dependent position differences quickly appeared. However, the forward speed variation among the initially bogussed TCs subsequently declined as a progressive homogenization harmonized the initially supplied structural differences. The homogenization likely involved model physics such as microphysics. This result casts doubt on the ability of models to retain and propagate forward information supplied at the initialization by advanced data assimilation techniques or parameterized vortex wind profiles. Asymmetries in near-core convective heating emerged as an important structural aspect that survived the homogenization tendency. The bubble and bogussed TCs developed markedly different heating patterns, which appear to help explain why the artificially-established storms tended to move about three times faster than their bubble counterparts. The reasons for this are not presently understood fully.