I think for nearly 30 years I’ve used TeX style quoting for double quotes in anything I wrote using ASCII text.

 ``Quoted text.''

Now that I’ve adopted Markdown for nearly anything that I enter as ASCII that’s intended to be English text (probably rich text), I’ve also, finally, decided to use the double-quote character. It’s true that the ASCII double quote doesn’t explicitly specify whether a left- or right-double quote is intended, but the implication is usually clear enough and (hopefully) rendering code is now smart enough to do the “right thing.”