The cable routing is correct for this style of BB. No plastic or chromed metal guide is used. The guides are built into the cast shell. The paintwork does get worn away. I have this style on my Bob Jackson tourer.

Drainage holes in the BB are not only to prevent the frame from rusting. They also prevent the bottom bracket bearings from running in a water bath. Many of these classic designs were built when BB bearings were 1/4" cup and cone. They had a plastic protection sleeve but otherwise poor sealing.
Cartridge style BB units (eh Shimano) do not have any openings inside the shell so water would not affect them. There are some rebuildable cartridge bearing units that would be affected by running in a water bath. Their seals are not that good.
In practice, nothing gets into the shell and if it did, it would drain out.