The important thing to note was that, like in many wargames of the period, the most salient information was in the table referenced. With the table doing all the math, how the armor is classified is somewhat superfluous; they could have just called Armor Class A, B, C, etc. The central design conceit is that you're trying to keep the target numbers "on the die," so that you can just roll, see the result, and know the outcome. Arneson & Gygax just happened to use ordinal numbers for the classes, which allowed for further expansion using negative numbers.
THAC0, then, was just a later innovation from people noticing, "Hey, the to-hit numbers go down by one counting armor class from 0, so if you subtract the Armor Class number from the to-hit number for AC 0, you get the to-hit number for that AC." And from there, "So if you roll a d20 and subtract the result from the to-hit number for AC 0, you get the number for the lowest AC that you can hit!" And they started using that so they didn't have to reference the tables. Then, that shortcut was put into the official game.
The innovation of 3e was its embrace of "imaginary die results". By which I mean, you have an attack bonus of +7, and your opponent has an AC of 21. Not only is the target number "off the die", but so is the final result if you roll a 14 or higher. This is certainly a cromulent way of doing things (though things got out of hand in 3e and 4e, IMO, when AC and attack bonuses could be so high, that the die roll was a proportionately smaller contributor to success).
But such a system (and THAC0 for that matter) would have been thought inelegant from a design perspective in 1970s wargaming culture. Why make the participants do math in their head in the first place, when you can just get all the math out on a table, and a few plusses or minuses notwithstanding, roll the die and immediately see if you were successful or not.