Silicon carbide (SiC), a third-generation semiconductor distinguished by its ultrawide bandgap, high critical breakdown field, and superior thermal conductivity, has become indispensable for next-generation power electronics and radio-frequency devices. However, achieving high-aspect-ratio microstructures in SiC demands etching techniques that simultaneously ensure atomic-level precision, minimal surface damage, and process scalability. This study presents a breakthrough in chlorine-argon (Cl2/Ar) plasma-based atomic layer etching (ALE) for 4H-SiC, addressing critical challenges in conventional inductively coupled plasma approaches. Through systematic investigation of surface modification and modified-layer removal mechanisms, we developed an authentic continuous ALE protocol with good self-limiting behaviors. The optimized process achieves an excellent combination of performance metrics: an etch rate of 13.2 Å/cycle (70 s cycle time), sub-8 Å RMS surface roughness within 15 cycles, and effective repair of plasma-induced sidewall surfaces. This work expands the understanding of the mechanisms involved in SiC ALE and establishes a scalable pathway for fabricating SiC devices with reduced ion bombardment damage, opening new frontiers for high-frequency power modules and radiation-hardened MEMS applications.