The reduced dielectric screening in atomically thin transition metal dichalcogenides allows to study the hydrogen-like series of higher exciton states in optical spectra even at room temperature. The width of excitonic peaks provides information about the radiative decay and phonon-assisted scattering channels limiting the lifetime of these quasi-particles. While linewidth studies so far have been limited to the exciton ground state, encapsulation with hBN has recently enabled quantitative measurements of the broadening of excited exciton resonances. Here, we present a joint experiment-theory study combining microscopic calculations with spectroscopic measurements on the intrinsic linewidth and lifetime of higher exciton states in hBN-encapsulated WSe₂ monolayers. Surprisingly, despite the increased number of scattering channels, we find both in theory and experiment that the linewidth of higher excitonic states is similar or even smaller compared to the ground state. Our microscopic calculations ascribe this behavior to a reduced exciton-phonon scattering efficiency for higher excitons due to spatially extended orbital functions.