but can't you just use the quotation mark/apostrophe key?
No. It is as incorrect as using a feet mark instead of an apostrophe.

Because more people use quote marks and apostrophe's than foot and inches marks, most programs automatically use curly quotes and apostrophes. But it is often necessary, giving the size of a painting, or other artwork, to provide the measurements in feet and inches, and 8' 9" is not correct if you use curly quotes and apostrophes (though it seems to be correct here).