No coat needed! That's what my late father thought, until the night he broke down on an expressway in the peeing rain and had to either try to fix it on the shoulder with only a dim torch (it was the 1980s) or walk to a phone.
You only think driving is easier because you've made driving extra easy and cycling unnecessarily cumbersome. If you won't put the rucksack in a more accessible place, store the bike more slickly and bolt on some real lights that don't need charging, why not level things up by putting your car keys in the loft, parking the car sideways on the drive and unplugging the headlight bulbs?