Earlier quoted context omitted.
Interestingly, the logic of mapping of two single quotes into a double quote was not built into TeX; rather, the metadata in each of the standard fonts simply used the ligature mechanism to handle it, just as they would specify that "f" followed by "t" should turn into the single-character "ft" ligature. It's a shame that ASCII (and its visual representation on terminals from most manufacturers) has a wonderfully sla…
About your middle paragraph: note that ASCII doesn't have left and right quotes; at 0x60 it has GRAVE ACCENT ` (not a left quote), and at 0x27 it has APOSTROPHE ' (not a right quote). Unfortunately for many years, fonts and terminals (like the SAIL ones you mentioned) continued to encourage abusing these characters as symmetric left- and right-quotes (as they were in some character sets pre-ASCII and even an early ve…
For starters, most easily at hand, see Communications of the ACM, Vol. 8, No. 4, April 1965, page 207, which shows them by those names.
Of course, there are details. It says that the 0x40 character can also be used as a grave accent, but only if "preceded by an alphabetic character and a BS (Backspace) in that sequence." Oh, for the days of hard-copy terminals.
And 0x27 is worse. It is documented there to be used as Apostrophe, closing single quotation mark, and even acute accent (but again, only in the context of the three character sequence alpha-backspace-accent).
Fine, that was 1965, and no controversy. But following the actual ANSI standard along over the years, by 2007 they're still there in "Coded Character Sets - 7-Bit American National Standard Code for Information Interchange (7-Bit ASCII)" ANSI INCITS 4-1986 (R2007) / ANSI X3.4-1986 (R2007), Approved June 14, 2007; Table 7, page 12. (Well, in 1986 they'd been slightly renamed to be Left and Right Single Quotation Mark, so the names would make sense for right-to-left languages, too; just as Paren, Bracket, and Brace pairs had all also changed names from "Open/Close" to "Left/Right".) The subsequent revisions to the ASCII standard, of June 15, 2012 and November 2, 2017, I don't have copies of, but these character designations clearly lasted at least into the "updated definitions" current as of mid 2012.
So, left and right single quotes were clearly in the official standard for almost five full decades beyond "early ASCII". I expect that they survive still, and will soon go into their seventh decade, but happy to hear otherwise from anyone with access to the later standard documents.
(And, yes, of course the Unicode standard has its own (no doubt better) opinions about what goes on with the first 128 characters out of tens of thousands, and what they're called and what they're properly used for; but that's a different issue than what the ASCII standard itself has to say about cramming stuff into its overloaded character set with a grand total of 128 slots.)