Tom,
If the inner cable insulators are still in good shape, you're probably OK for the occasional contact with the cable. Still, I would be worried about someone leaning a metal ladder against the cable, or accidentally cutting the wire when scraping the walls for repainting. Sounds dumb, I know, but people do all kinds of odd things and accidents happen.
Codes are generally the bare "minimum" required for safety. That doesn't always mean it is the best way to handle it. Even though it may meet code and be common in your area, the fact your cable has deteriorated like that is a huge warning flag to me, code or not.
All things considered, conduit is cheap. I don't see any reason NOT to use it in an exposed location like that, and plenty of reasons why you should. But, enough preaching, I know it wouldn't be a simple or inexpensive task at this point to update everything.
Quick fix, remove as much of the cracking insulation as you can (to avoid puncturing any new repairs), then wrap it well with electrical tape. I know they make heat shrinkable tape, but I have no idea who carries it these days. You would also need a heat gun for that.
If I were going the quick fix route, I would pick up some conduit and cut it in half lengthwise. Then I would install it as a protective cover over your existing cable. It would provide additional physical protection, and block sunlight from further deteriorating the cable. It would block rain to some degree too, but would allow drainage at the bottom if needed.
Good luck with your project!
Anthony Watson