If you're in something other than C or Am, you're supposed to use key signatures to point that out and clean up the notation. C/Am is just the default.
"Standard musical notation is ambiguous when used on guitar", actually it isn't if you mark strings and fingerings as needed. This is widespread practice, each instrument has its own "tweaks" on the basic system. Standard notation in particular is quite hard to work with on guitar, and one can see why so many people just rely on tablature - but ambiguous it's not.
Chord charts may be "concise" but they don't actually convey harmonic structure very well, not least because of the multitude of informal conventions and the ambiguity that these create; figured bass notation (while admittedly not very well known) does a far better job of it overall. For example, "walking" bass lines become immediately apparent in thoroughbass.