The earliest usage of this rating that I’m aware of was by Moody’s in its bond-rating books from the first decade of the twentieth century. (For example, Moody’s Analysis of Railroad Investments 1909.) Its highest bond rating was (and still is) Aaa. Its competitors spelled their highest rating AAA.
There were precursors. This book of ratings of Canadian merchants from 1864 used a rating of net worth (“pecuniary strength”) from A1+, A1, 1, 2, 2½ and so on down to 4, with a separate credit rating topping out at A1. By 1869, the net-worth rating was changed to A+, A, B, C and so on (with equivalents given for the previous system.) The references to the old system were dropped in the 1876 edition. In the 1879 edition, on page 4, you see a new rating, AA, was added above A+, so that the existing typesetting would not need to be changed—an expensive proposition in the days of metal type! Hence AA saying “$1,000,000 or more” and A+ unchanged from “$750,000 or more.”
A possible reason to use multiple letters in the late 19th century was so that they could be transmitted quickly by telegraph, although some systems used a combination of letters and numbers. Some nineteenth-century directories come with keys of abbreviations to use over the telegraph for fast transmissions—not published ratings, but substitutions for telegraph operators to be able to type more quickly in Morse code, such as X for excellent credit and XA for high. A more verbose version can be seen starting on page 90 of this book. “Lot” is code for high credit, “Noah” for good credit, “Pharaoh” for fair credit, “Abel” for no credit. and “MASSER” for “Come here at once, we fear an absconding by”. It was the original compression algorithm for telecommunications.
Since 1946, the second-highest level of baseball in North America (after the major leagues) has been called AAA. A number of minor leagues wanted to invent a new term to designate themselves as better than the two levels that had previously existed, which were reorganized as A, AA and AAA. A similar system is used by the US Department of Agriculture for eggs (although the grades are AA, A and B). Tbere are also AAA batteries, although these designate size and voltage rather than quality.
You can think of this as a form of grade inflation. the ratings agencies didn’t want to scare buyers off by giving a grade of C or D (considered mediocre to bad in school) to what was supposed to be an investment-grade bond or a safe and healthy, but not pretty, egg, so they invented ratings higher than A. (Teachers would adopt a different system: A-, A, A+, sometimes A++.)
As a result, A is almost never the highest mark in a grading system. It usually comes to designate something good, and then at least one grade above it gets added for superlatively good. Sometimes this is A+, AA or A1. However, if there is an AAA rating, it is always the highest. Some gaming magazines from the ’90s gave games letter ratings, and these were notorious for being inflated, which might help explain why the industry settled on a superlative much-better-than-A. A+, five-star, 100% or 10 were all ratings given out by some gaming publications, but to the best of my knowledge, no one was handing out AAA, AA or BAA game ratings that could be confused with this usage. People might also have wanted to avoid a mix-up with the slang phrase, “bring my A-game.”
Another use of “AAA” was that customers used to look up businesses in a telephone directory that listed all the businesses of each type, alphabetically. Naming your business AAA was therefore the equivalent of getting the top hit on a Google search.
The comic strip you quote is referring to something else entirely: the road maps sold by the American Automobile Association.