A new local hybrid functional, LH20t, with a position-dependent exact-exchange admixture governed by a simple local mixing function (g(r) = b·τW(r)/τ(r)), combined with gradient-corrected (PBE) exchange and meta-GGA (B95) correlation, as well as a second-order GGA-based pig2 calibration function to address the ambiguity of exchange-energy densities, has been constructed. The adjustable parameters of LH20t have been optimized in a multistep procedure based on thermochemical kinetics data and measures of spurious nondynamical correlation. LH20t has subsequently been evaluated for the full GMTKN55 main-group energetics test suite, with and without an added DFT-D4 dispersion correction. Performance of the new functional in the GMTKN55 tests is excellent, better than any global hybrid so far, approaching the best results for any rung-4 functional, without any noticeable artifacts due to the gauge ambiguity. The robust performance across the board is combined with enhanced exact-exchange admixtures of >70% near the nuclei and asymptotically (but low admixture in bonds). This helps to provide excellent performance for a wide variety of excitation classes (core, valence singlet and triplet, Rydberg, short-range intervalence charge-transfer) in TDDFT evaluations. Notably, LH20t is the first functional that provides simultaneously the correct description for the most extreme localized and delocalized cases of the MVO-10 test set of gas-phase mixed-valence systems. This outstanding performance for mixed-valence systems, which signals a very fine balance between reduced delocalization errors and a reasonable description of left-right correlation, is corroborated by tests on ground- and excited-state properties for organic and organometallic mixed-valence systems in solution.