Unless I've missed something, it seems to me that since you'll be ranked for each role, and that matchmaking will reflect your skill in the role you are assigned, players swapping roles in champ select will really screw over this system.
First, if I say play Mid primary and Bot secondary, and am given Bot (or filled somewhere) in a game, but I ask if I can mid, and the mid person says ok (as happens from time to time) I'm going to be playing mid but the game will count to my bot rank. This could be fixed I guess by having the game work out where you're playing, rather than what you were assigned, but the next issue is the real killer.
Second, if matchmaking takes position to account, if I am say, a Diamond level Mid, but a gold level adc, and get given bot, my skill for matchmaking will be taken as that of a gold player. However if I swap roles to mid, I am now a diamond player, playing in a gold game, which is a real screw up for the system, and would make for a horrid experience for the 5 enemies, especially the mid.
Another issue I see with this, is as for me, I play mid pretty much exclusively, except when I have to play another role because im placed in my secondary or filled, and the mid didn't want to swap, so with this system, when I'm filled or given bot, the game has significantly less meaning for me, since it won't contribute to my mid main rank. This not only makes the game feel less engaging for me, but also means im less likely to try as hard as I would usually, since its almost like a normal for me, not affecting the rank I care about.
Please riot don't go ahead with this rank per role thing, its really dumb and has many flaws, 2 I've mentioned but others in other posts too