An excellent electrostatic control has been early on identified as one of the most critical ingredients to build band-to-band tunneling field-effect transistors (TFETs) with a steep sub-threshold swing (SS) and a high ON-current (I_ON) [1]. These essential features can be obtained by reducing the thickness of ultra-thin-body structures or the diameter of nanowires. Two-dimensional materials, especially their single-layer (SL) configuration, represent a promising alternative to conventional semiconductors due to their intrinsic sub-1nm thickness. Indeed, a TFET implementing an atomically thin MoS₂ channel combined with a Ge layer was recently shown to exhibit a less than 60 mV/dec SS over several orders of magnitude and a decent ION [2]. In this experiment, however, MoS₂ had to be grouped with Ge to achieve the desired goal, thus raising the question whether 2-D materials alone can provide a suitable platform for high performance TFETs. Various theoretical studies based on empirical tight-binding models and focusing on SL transition metal dichalcogenides (TMDs) [3] and black phosphorus [4] have come to the conclusion that these compounds, in particular WTe2, could deliver ON-currents larger than 100 μA/μm at a supply voltage V_DD=0.5 V and OFF-current I_OFF=1 nA/μm. Here, by employing an ab-initio quantum transport simulator, we will demonstrate that none of the usual TMDs reaches a I_ON >>10 μA/μm, contrary to recently discovered 2-D materials [5] that could pave the way for future, highly efficient TFETs.