I'm going to answer this purely from a D&D perspective, as this is my area of expertise.
The idea of 'descending armor class' in D&D comes from the 'alternative combat system' presented on p 19 of the first D&D book Men & Magic (1974). Here the armor classes given range from 9 (no armor or shield) to 2 (plate armor and shield), with the other column having the to-hit number on a twenty-sided dice for fighting-men (sic) of groups of levels 1-3, 4-6 up to 16+.
The armor categories in the 'alternative combat system' closely mirror those of the Man to Man Melee table on p 41 of Chainmail, the game which in theory was needed to play the first edition of D&D, but in fact could be sidestepped with the 'alternative combat system'. The Chainmail table differs however in that no numbers are given to the armor classes, only descriptions (e.g. "No armor", "Leather or padded armor"), and compares this to the weapon being used to attack, there being no concept of class or level in Chainmail. The 'Individual Fires with Missiles' table on the same page of Chainmail actually refers to these as 'class of armor', but with an ascending numbering system, from 1 (corresponding to no armor) to 8 (corresponding to plate armor and shield).*
In the OD&D 'alternative combat system', to hit progression against certain armor classes was not completely linear as you advanced in level, nor would it be so until the idea of THAC0 was made part of the official rules in the AD&D 2e Player's Handbook (1989) and Dungeon Master's Guide. (THAC0 is mentioned in an appendix to the AD&D 1e DMG, but still the tables for hits against certain armor classes are not completely linear in AD&D 1e). From OD&D to AD&D 1e the rules assumed you would consult a table to calculate your hit probability.
By the time of AD&D 2e the idea of to-hit against armor class had become nothing more than a calculation. Your THAC0 decreases in even steps depending on your class and level. Then: THAC0 - AC = to hit number. See for example p 89 of AD&D 2e PHB. From here it was a short step to the much simpler system of an ascending armor class equalling the to hit roll, with modifiers added to or subtracted from this roll, which was first introduced in 3e (2000 ff).
So there was no particular advantage to the 'descending armor class' system. It had just developed historically from its roots in Chainmail from being a 'this weapon against that armor' to a 'this level of ability vs that armor' calculation. Mathematically there is no difference between the principles of AD&D 2e (descending) and D&D 3e (ascending) armor classes, once a graded THAC0 increase by class and level was introduced and players no longer had to refer to tables to calculate the possibility of a hit.
* Thank you to Jon Peterson for highlighting this last connection. For a much more detailed discussion of the historical development of armor class see his book, Playing at the World (2012), and for his treatment of armor class in the various editions of Chainmail, see: http://playingattheworld.blogspot.com/2012/10/armor-class-in-chainmail.html