This sounds extremely odd. I seriously doubt a usb cable can be too short to charge something., What is perhaps odd, but more likely, it sounds like an extremely odd incompatibility. But I wouldn't expect that with power. But if it is an incompatibility for some strange reason then by that I mean either your car adapter is picky, or your usb cable is picky. The picky device would be the nuisance. As car chargers and usb cables are cheap, you could try some short cables from another source, and a car charger from another source.
I have had incompatibility type problems with USB-Ps2 adaptors, and I chucked a whole load 'cos they worked well in one computer but not another. I kept the lot that worked in any computer.Tthey were dependent on data and power, I always assumed they were getting power and the incompatibility was maybe data related. Perhaps it can affect power though. In which case your incompatibility is less strange but still strange. All I can suggest is getting another car charger and short cables from another source.
I can't explain the incompatibility other than to say i've had what might be a similar incompatibility related to USB, and I think incompatibility is more likely than a diagnosis that short cables won't carry the power. It looks like you've diagnosed that it's not strictly one or the other (cable or car adapter) that is all bad.
So i'd troubleshoot for an incompatibility. Though that would require buying more of the cheap things. more car chargers more short usb cables (in both cases, from other sources).
You might find a charger that works with some small usb cables and you might find a particular charger tends to work less than others with cables, or a particular charger works with almost any of the cables, and similarly with the cables. So then you can keep the ones that are lenient and chuck the ones that are strict. Such is the nature of incompatibilities based on my somewhat similar experience of USB-Ps2 adaptors (though I didn't chuck out the strict computers in favor of my lenient computers! I merely kept the lenient USB-Ps2 adaptors which worked with any of my computers even the strict ones).
You could go further and test with a multimeter, or you could see if a USB voltage meter (google that for a pic) gives you any clues. But that shouldn't be necessary as you know if you're getting power to your phone based on whether it charges.