You can't expect run a 2k junker on significant monthly miles without incurring costs. You might be lucky, but it's a bad bet. Not to mention the risk that some mechanical failures may cost you your job.
Old cars are definitely cheaper to run (net) than new ones, but they aren't free.
This shouldn’t be as much of an issue, compared to the ride share market, as you can make deliveries in a $2k junker for years before it gives out.