Do the films ever show other robots of that type? I'm wondering if they are all the same - and whether the films ever show the designer?
The sequel novels shows other protocol droids, and I seem to recall most of them showed some sort of 'fussiness'. IIRC, at least one was stated as being in-universe based on C3PO (as it was a translator droid for Chewie's nephew until his non-Wookiee friends learned to understand Wookiee), so that complicates matters. Especially as the series was a deliberate 'Star Wars: The Next Generation' (in addition to Chewie's nephew, it also featured Han and Leia's twin kids), so giving C3PO a 'child' in a sense could have been a deliberate choice of the writer.
The Phantom Menace has that a 9-year-old Anakin Skywalker assembled C-3PO out of spare parts so his mother could have help dealing with the aliens that frequented Tatoonie on business. Whether he wrote the programming, or just scavenged that as well, isn't specified. Presumably since other protocol droids exist, the programs are around, or hard-coded into whatever processors are used -- Anakin then wouldn't be a designer as much as modifying existing (non-functional) droids to get one that worked.