I don't like this idea at all.
That means you have to grind out of elo hell on all five roles, instead of grinding out with one role then getting to enjoy quality games on multiple roles.
Nevermind that you can't actually climb the ladder out of bronze/silver by playing support the way it's meant to be played. You only climb out of low elo by playing a carry in a support position.
How is an ADC suppose to feel suffering through low elo hell at the mercy of ther incompetent team, yearning for the day they can break out and really show what their ADC skills are once they have proper teammates?
I also think it's bad from an organization perspective because it presumes that positions like top have clearly defined roles and playstyles - but they don't really, especially the lower elo you go. It's a grab bag of all kinds of stuff. Mid to some extent has become like that too.
I can play Talon just about as well top or mid - But it's the same playstyle in either position. I'm not a mid player or a top player, im a Talon player. An overall rank better fits that than a positional rank.
I think it's also a fools errand of a quest, because almost nobody plays multiple roles from the perspective of them being roles in themselves. Not so much because of the role limitation, but because of champion limitations - It's better to master a few than play a wide diversity if you want to climb. It has little to do with the role itself. Someone might be an expert with one champion who happens to play top lane mostly but can play multiple roles, but they are not necessarily a toplane expert in general. That person might crush jungle on their champions just as well as top lane, but not be placed at the appropriate skill level. That same person who is so highly ranked top may fumble all over themselves if their one trick champion gets banned. They aren't really a "top laner" in the sense of being well versed in the role itself. They are a one trick champion player.
I think only jungle, support, and ADC have clearly defined enough roles that ranking them specifically makes sense. They all basically have the same goal and playstyle.
Mid and Top are so varied, and with the state of the way the game is, they really have no role other than don't feed and try to do whatever you can to help snowball bot lane. Just about anything can fit that description, and what you pick may be more dependant on what your team comp needs for teamfights than what the role itself needs.
This whole scheme also fails to take into account the extent to which how experience in one role transfers to another. A challenger level player might main mid, but I guarantee you they will crush any bronze level game from any position. It's not going to be a fun experience for the other players getting paired with what is essentially a challenger smurf just because they only focus on ranking up one position.