We report improvements in the growth characteristics of AlGaN/GaN heterostructures on 4H-SiC substrates using plasma-assisted molecular beam epitaxy. Employing recently established N-rich growth conditions at temperatures in the thermal decomposition regime of homoepitaxial (0001) GaN, this method proved successful for the reduction of threading dislocations in heteroepitaxial growth on SiC by simultaneously preserving good surface morphology free of excess Ga. This self-recovery of surface morphology at high growth temperatures overcomes the restrictions of using two-step GaN buffers as common under Ga-rich conditions. Initial results from unoptimized high electron mobility transistor structures grown under this approach exhibit decent mobilities, output powers and associated power added efficiencies larger than 1330 cm2/(V s), 7 W/mm, and 50% at 48-V drain bias, respectively.