Band structure engineering has a strong beneficial impact on thermoelectric performance, where theoretical methods dominate the investigation of electronic structures. Here, we use angle-resolved photoemission spectroscopy (ARPES) to analyze the electronic structure and report on the thermoelectric transport properties of half-Heusler TiCoSb high-quality single crystals. High degeneracy of the valence bands at the L and Γ band maximum points was observed, which provides a band-convergence scenario for the thermoelectric performance of TiCoSb. Previous efforts have shown how crystallographic defects play an important role in TiCoSb transport properties, while the intrinsic properties remain elusive. Using hard X-ray photoelectron spectroscopy (HAXPES), we discard the presence of interstitial defects that could induce in-gap states near the valence band in our crystals. Contrary to polycrystalline reports, intrinsic TiCoSb exhibits p-type transport, albeit defects still affect the carrier concentration. In two initially identical p-type TiCoSb crystal batches, distinct metallic and semiconductive behaviors were found owing to defects not noticeable by elemental analysis. A varying Seebeck effective mass is consistent with the change at the Fermi level within this band convergence picture. This report tackles the direct investigation of the electronic structure of TiCoSb and reveals new insights and the strong impact of point defects on the optimization of thermoelectric properties.