I'd hardly say "we have symbols for everything".
The reason this is not a good idea is that the word "example" is not used in any context other than its natural language meaning; in contrast, "for all", "there exists", "implies", etc. are phrases which mathematicians want to use inside the mathematics, via the symbols $\forall$, $\exists$, $\implies$.
There is no added benefit to having a symbol for "example"; using a symbol that serves no purpose other than to replace an English word, outside of the mathematical content of a discussion, just creates a barrier to understanding.