Hybrids -- as distinct from "plug-in hybrids" (PHEVs) -- aren't using the ICE as a backup; the ICE is the original source of all of the car's energy.
The hybrid just recaptures the car's kinetic energy during braking and coasting, and uses it to charge a battery. The power generated runs all of the car's electrics, and can be used as supplemental motive power, or even exclusive motive power for short distances at low speeds.
This has other benefits -- the ICE can be optimized more for fuel economy instead of power (a/k/a the "Atkinson cycle" engine), and you can get away with a smaller ICE anyway, since you have electric assist for quick starts from stop.
This is in contrast to a conventional car, which mostly wastes energy in braking and coasting by turning it into heat and worn brake linings.
Good point about the ICE being the source of all power in the car.
But doesn’t the ICE shut off and the hybrid runs all-electric in city driving? Then the ICE turns on to charge the battery? Or does the ICE run 100% of the time like a diesel locomotive?