The big mechanical advantage in simplicity is the transmission. While they’re called “eCVTs” in some cases, the transmission is better described as “almost no transmission”. They do not use the same belt and cone system that gasoline CVT vehicles use.
In Toyota systems they use a simple fixed planetary gearset and can vary the output speed simply by varying the ratios of speed of the two electric motors and the gasoline engine, rather than mechanically changing the ratio of the gears like a traditional transmission.
The Honda hybrid system is even more simple. They just directly drive the wheels with an electric motor and use the gasoline engine as a generator. (With the exception of a single lockup clutch that allows the engine to drive the wheels at a fixed ratio at highway speeds)
Hyundai is a weird exception. Their hybrids have traditional transmissions attached to them.
Except for some computerized parts of the system, the majority of them can be worked on by any mechanic, or even shade tree mechanics. The high voltage system requires care, but there are simple procedures to work on it safely. You can find many YouTube videos with instructions on tasks like rebuilding a battery pack, that dealers won’t even do. Most parts on a car aren’t the high voltage system anyway.
The amazing thing about them is that they have no parts that need friction to work like belts, CVT axles or even the clutch. Nor do they have any moving parts like a regular transmission which shift into place.
It's 2 electric motors connected via a planetary gearset to the ICE. Nothing can get out of alignment or get loose.
Parallel hybrids ICEs are just as complex as normal ICEs.
I'll add that hybrids are more profitable for any manufacturer because it means that you can't take it to your family mechanic for service (You need special training and equipment to work on them because it's high voltage). Because the dealers are making a lot on service, the manufacturer can cut their bonus on sales.