How fast is the engine turning over? Backplates designed for electric starters are geared down, because electric starters are (relatively) high-speed low-torque devices. Power drills OTOH are low-speed, high-torque devices.

Single-speed cordless drills are typically 0-1000rpm, and 2-speed types are usually 0-2000 (in high speed mode). I can sometimes start my engine with a 2-speed cordless, but have much better luck with a mains drill at 3000rpm.