I get the impression that the designers normally do more than just signs - depending on the employer, they may also do traffic signal plans (for bidding, not the planning of where signals go/warrant analysis) or any other roadway plan sheet.
Traffic design is its own functional discipline, but in addition to signing and signals, it can also include lighting, guardrail, ITS, etc. Not all of a traffic designer's work product goes into construction plans either. Depending on how the sign procurement process is structured in a given state DOT, it can also include producing work orders showing each sign at a much higher level of detail (and with more thorough dimensioning) than on the plan sheet.
I don't think I have ever met a traffic designer who did nothing but signs all day long, but I wouldn't rule out the possibility of that level of specialization in, e.g., a dedicated sign design unit such as some state DOTs (e.g., MoDOT) have.
I would imagine that a traffic designer who was interested in sign design from a hobby perspective, not just as a way to earn income, would get more satisfaction from being able to work with tools which make it simple to produce pattern-accurate sign layouts, sign panel details, and sign elevation sheets. State DOTs vary widely in the types of signing sheets they require to be included in signing plans and also in the tools they specify or make available for this purpose. The state DOTs that produce the majority of the signing sheets I work with conform to a three-part model--sign layout sheets, sign panel detail sheets, and sign elevation sheets for overhead signs only--but this is far from universal. Some state DOTs produce sign layout sheets only, like Louisiana DOTD and Wyoming DOT; others, like Colorado DOT, produce just sign layouts and sign elevations (what CDOT calls "sign cross-sections"). A few state DOTs like clean signing sheets and go so far as to specify their preferred design packages (Arizona DOT accepts only
SignCAD, while others have standardized on
GuidSIGN), while others (Montana, for example) have never produced pattern-accurate details for designable signs. Plus, as time goes on, state DOTs change how they structure the signing sheets in their plans sets. Ten years ago, Caltrans, KyTC, and NCDOT never used to include sign panel detail sheets in their plans sets--now they routinely do.
A liking for sausage doesn't mean you would be happily employed as a butcher.