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Over the last few years, $ab~initio$ methods have become an increasingly popular tool to evaluate intrinsic carrier transport properties in 2D materials. The lack of experimental information, and the progress made in the development of DFT tools to evaluate electronic band structures, phonon dispersions, and electron-phonon scattering matrix-elements, have made them a favored choice. However, a large discrepancy is observed in the literature among the $ab~initio$ calculated carrier mobility in 2D materials. Some of the discrepancies are a result of the physical approximations made in calculating the electron-phonon coupling constants and the carrier mobility. These approximations can be avoided by using a sophisticated transport model. However, despite using appropriate transport models, the uncertainty in the reported carrier mobility is still quite large in some materials. The major differences observed between these refined model calculations are the `flavors' of DFT (exchange-correlation functional, pseudopotential, and the effect of spin-orbit coupling) used. Here, considering several monolayer 2H-TMDs as examples, we calculate the low- and high-field transport properties using different `flavors' of DFT, and calculate a range for the electron mobility values. We observe that in some materials the values differ by orders of magnitude (For example, in monolayer WS$_{2}$ the electron low-field mobility varies between 37 cm$^{2}$/(V$\cdot$s) and 767 cm$^{2}$/(V$\cdot$s)). We analyze critically these discrepancies, and try to understand the limitations of the current $ab~initio$ methods in calculating carrier transport properties.