There are certainly enough old diesels out there and enough people willing to go around collecting old oil to keep a small number of people occupied and mobile.
It is also not really a viable large scale solution to "how do you move people around?"
There are lots of really good answers (walking, public transit, electric bicycles) but one obvious answer is "cars" and electrifying those is probably a good solution.
Electricity can be generated from fossil fuels more efficiently at large scales than small (a power plant produces less CO2 than a car for a given amount of work). Electricity can also be generated by extracting "free" energy from the environment (wind / solar / hydro / dogs on treadmills). The distribution system for electricity is already quite robust and is already everywhere, and people like cars. There's even lots of inexpensive electricity available at night, when most people aren't driving their cars. All we need is a way to get the power to the cars that park where people don't own the parking space.
Disposing of the waste stream of parts of the cars has always been a problem. Hopefully people come up with a way to solve it; there's enough valuable metal in a car battery that it is likely they will.
There are already all sorts of terrifying industrial processes which I can't imagine are possibly cost effective and yet they're the foundation of modern society. There are also all sorts of hideous "farm out the cost to someone else" processes relying on destroying somewhere else / poisoning someone else.
People refine gasoline by boiling crude oil in a rusting metal tank; people refine gasoline in trillion dollar oil refineries. Why and where and for who answers how it gets done.
Can one cost-effectively convert refined materials in a battery (cobalt / nickle / lithium) back into raw inputs for a new battery? Can it be done profitably by a child in a toxic fire pit or can it be done profitably by a chilled shredder in inert gas?
Not a simple problem, but probably one that can partially be solved with market incentives and partially solved by laws and partially it won't get solved. But we should probably try, right?