Chord symbols are more often the way they are through convention rather than logic. If a symbol causes an argument, I'd say that's already a flaw in communicating what the chord is trying to convey.
In this case, C7+ isn't too confusing. Without specifying a scale degree, "+" augments the 5th in any case I've seen. But you could also be augmenting 9ths or 11ths for example, so it doesn't hurt to explicitly point out +5.
If the author wanted Cmaj7#5 or Cmaj7+ or Cmaj7+5 etc, but wrote C7+, I'd ask them to change it. The augmented symbol is modifying degrees that are already stated, ie, C7 states R, M3, P5, m7, then "+" modifies the P5 to A5.