First and foremost, the transmission replaces the rather staggering pile of complexity of a modern automatic transmission, typically, with "a few motor/generators, some planetary gears, maybe a band that only engages when a motor is already stopped, and some power electronics." Compared to the 9+ speed automatics, this is dramatically simpler. Quite a few hybrids don't even have a mechanical reverse gear, it's just using the electronics for that brief period.
But, beyond that, you generally aren't asking the engine to idle, or to provide "starting torque" for the car - the hybrid system handles that sort of thing well. On at least the Gen 1 Volts, the motor "idles" at about 1200-1300 RPM, vs the ~750 RPM in most other vehicles, because it's almost never needed at low speed (heating in the dead of winter is the one time I notice it). But you don't have low speed, high load operation on the engines (which is a hard regime to operate in), and you don't have rapid speed changes with gear shifts (which is certainly more stressful than smooth speed changes or continuous speed operation).
You have less brake system wear, and... it goes on.
I know there's this popular "Hybrids/PHEVs are the most complicated of both worlds, so they must be the most unreliable of all worlds!" thing going around, but the data is quite clear that they're exceedingly reliable in actual use, and the "most complicated of all worlds" things tends to zoom out far enough to avoid looking at the transmission or engine design at any level of detail.