In case you don't have the time, it's been a while since I watched these, but IIRC, the stability of the coaxial escapement comes from the pushing/rotating action of the jewels against the escape wheel rather than sliding as in a Swiss lever, and the degradation of oil over time. With a Swiss lever, as the oil becomes stickier over time, the sliding action of the escape wheel teeth across the pallet jewels results in changes in timekeeping characteristics. With the coaxial, the rotating/pushing action slides considerably less, and is thus considerably less affected by oil degradation. Since it's not/less subject to changes over time due to changes in lubricity, it's more stable.