The recent Technology Connections video[1] on Toyota's hybrid drivetrain claims that people misunderstand the purpose, and I had. I assumed battery for stop-start city driving and engine for everything else, but no. Only the motors can move the car which means no gearbox or transmission, which is simpler and cheaper than I had imagined two drivetrains would be. It has a small engine because the battery assists when power demand is high (acceleration) which is cheaper than a pure ICE car and the battery is smaller and cheaper than a pure EV. It (sometimes) starts the engine after pulling away because it needs enough charge to keep power available.
Two extra benefits: regenerative braking reclaims some energy, and the engine can run on the Atkinson-cycle which is too gutless for an ICE car. Both contributing to much better fuel efficiency than an ICE car, while keeping the convenience of easy refuelling instead of recharging.
[1] https://www.youtube.com/watch?v=KnUFH5GX_fI - "It's a really good idea and everyone hating on it probably doesn't understand it"