We report 491 new near-infrared spectroscopic measurements of 420 Near-Earth Objects (NEOs) collected on NASA's IRTF in the context of MITHNEOS (PI: DeMeo). The measurements were combined with previously published data (Binzel et al. 2019) and bias-corrected for albedo variations to derive the intrinsic compositional distribution of the overall NEO population. We also investigated individual subpopulations coming from various escape routes (ERs) in the asteroid belt by use of the dynamical model of Granvik et al. (2018). The resulting distributions reflect well the compositional gradient of the asteroid belt, with decreasing fractions of silicate-rich (S- and Q-type) bodies and increasing fractions of carbonaceous (B-, C-, D- and P-type) bodies as a function of increasing ER distance from the Sun. The compositional match between NEOs and their predicted source populations validates dynamical models used to identify ERs and argues against strong composition change in the main belt between approximately 5 km and 100 m. An exception comes from the overabundance of D-type NEOs from the 5:2J and, to a lesser extent, the 3:1J and ν6 ERs, hinting at the presence of a large population of small D-type asteroids in the main belt. Alternatively, this excess may indicate spectral evolution from D-type surfaces to C and P types due to space weathering or point to preferential fragmentation of D-types in the NEO space. No further evidence for the existence of collisional families in the main belt, below the detection limit of current main-belt surveys, was found in this work.