The biggest problem with super-cheap cars are the regulations and expectations they have to meet. A new car these days with no air bags? Probably not going to fly. No heat / defrost? Not going to be sold in the Northern states. Super-cheap, possible unreliable drivetrain? Might end up costing more in the end than the car's worth.
And then there are the small conveniences that need to be weighed against the extra cost. Power locks, power windows, etc. - even on a super-cheap car, they should still be offered as options to attract more potential buyers.
By the time you get done, you'll end up with something that looks similar to a bare bones Hyundai Accent, basic Chevy Cobalt, no-frills Ford Focus, etc. Sure, they all have some completely unnecessary creature comforts here and there (radios, speakers, AC, floor mats, etc.), but even if you removed all of them and changed the price to reflect the savings, I'd bet you still wouldn't be all that amazed at the price. And once again, a used car that's much nicer can still be found for similar cash.