It's an interesting idea and have some merit to it, but it can never outbest and outlast a normal bicycle. Still, it's significantly better than a car or motorcycle and depend on what sort of apocalypse we're talking about.

2)Peddling charges the batteries, so in an emergency you can turn on the battery

To actually charge the battery you need a voltage higher than the battery itself, and to charge the battery using the motor you will need something with regenerative braking, and to crank these motor you need higher energy than you normally do and put in to overcome the resistance in order to generate enough power to charge the battery. Even with regen braking in normal situation, i don't think it's enough to charge the battery. You'll be pedalling a significantly heavier bike in the end because of all that resistance.

3)The batteries can reasonably be charged by solar panels that a lot of houses have.

This is the true benefit of ebike, but you have to be in an apocalypse in a place with plenty of solar panel.

5)Generally easier to repair.

Compared to car or motorbike, yeah, but compared to a normal bicycle, there's a challenge if the electronics are fried or when battery need replacing.

The distance travelled on a full battery is absurd

This is true on eco mode, and depend on battery capacity, which affect the weight