Historically, the Plimsoll symbol (aka Plimsoll line) was created as hull mark that would serve as a ready indicator of whether a ship was overloaded and thus running too low in the water. It was later adopted by chemists to indicate standard state (currently defined by IUPAC as 1 bar).
Why was the Plimsoll symbol chose for this purpose? According to Wikipedia,
The plimsoll symbol (⦵ or
o) ... is used as a superscript in the notation of thermodynamics to indicate an arbitrarily chosen non-zero reference point ("standard state").
The language used by Wikipedia suggests it was chosen because it looks like a zero with a line through it, thus communicating "not zero". Applying this to enthalpy or free energy seems redundant and unnecessary, though, since by definition there is no true zero reference point for either (among state functions, this exists only for entropy). It's like having a special symbol attached to $ΔU$ to indicate that $U$ is conserved, when, of course, $U$ is always conserved.
Indeed, the problem with attaching a symbol to $U$ saying it's conserved is that it suggests that sometimes $U$ is not conserved (otherwise why would you need the symbol?). Likewise, attaching a symbol to $U$, $H$, or $G$ saying that the reference state is non-zero suggests sometimes it could be zero. I.e., I understand they needed a symbol for reference state. But I'm puzzled why they chose one that communicated "non-zero" instead of just choosing something that meant "reference", period.
Nevertheless, I'm sure these people knew what they were doing, and had good reasons for what they did. I just don't understand what that those reasons would be. I'd thus be interested to hear from anyone out there with knowledge of the history of this.
Perhaps the answer (here I speculate) is that they wanted to communicate the obvious (that thermodynamic reference states can never be true zero reference states) — and that the reason they wanted to do this was because they anticipated tables of thermodynamic values would be used by a broad audience, some of whom might not understand the underlying thermodynamic theory.