If ASCII had balanced quotes then they would be used by programming languages to delimit strings and we would be back to square one with regards to escaping them!
To use formal language theory, strings containing escape characters are regular, i.e. parseable with a finite-state machine. Allowing nesting means you need a stack to find the matching pair.
Even for things where the nesting does happen during lexical analysis, it's pretty trivial to keep a count in your lexer. Lots of languages support nesting comment syntax or string interpolation, which both have equivalent difficulty.
/* nested /* comments */ don't work */ (* nested (* comments *) work *)https://wiki.dlang.org/Commenting_out_code#Nested_comments
This allows commenting out code containing comments, which can be useful when debugging or giving usage examples in the code.
To end a string, use the » character.
?«Oh, you just use the « character.»
Parse error. Unexpected EOF.
To clarify: we’d still need escaping but in fewer cases.