Sigh-Fi

Bikes aren't great for tough terrain. They mostly require roads or paths. In a post-apocalyptic wasteland there would be a lot of those. But, the good thing that is that when the terrain isn't suitable for biking, you can get off and push the bike, or if truly necessary you can carry it. Meanwhile, if a highway is blocked and you're relying on a car, there's no way you're moving the car to the other side of the blockage.

The main benefit is that the parts are standard, maintenance is pretty easy, all the parts are sitting there, easily visible, so you can spot the problem and fix it. And if it's unfixable, it's pretty easy to swap for another part. Also, a bike with degraded parts still does a job. If you don't have working brakes, you can drag your feet. If you can't shift gears, you can just use the bike in whatever gear it's stuck in. If the wheel is dented, as long as it still rolls, you're probably ok. Pretty much the only things necessary are tires that aren't completely flat and a drive chain that has at least one working gear.