So I know it's come up many times over the years but now I want to talk about it.
The idea of "ranking" ARAM is a bit odd because ARAM is widely viewed as a "fun" mode for quick games that is heavily influenced by RNG and luck. However there is a lot of skill expression in ARAM as well. It strongly favors people with wider champion pools. It tests your ability to make comps work that no one with sense would put together intentionally. There are entirely different metas in ARAM many people don't even begin to understand. The RNG and luck factors generally go against most ideas of what a proper competition mode should rely on, however they are important to ARAM... otherwise you just have AM. ARAM accounts would also a problem without some changes.
So I've considered a few options to make it work without taking the AR out of Ranked ARAM. (any numbers may need to be changed a little or a lot)
The first change is largely to prevent ARAM accounts from dominating the ladder.
1. For Ranked ARAM every player chooses x number of champions to make up their ARAM champion pool. (Say 50 maybe?)
**_* (alternate: each player picks X number champions as the base for their pool, which is then filled out with 2X of the champions they play/know best (based on mastery or average performance grade or some other metric) and 2X of the champions they play/know the least_**
2. Remove rerolls for ranked ARAM. Autofill the "bench" on entering the lobby. (autofill bench either from entire LoL champion pool or 2 from each players ARAM pools) any player can swap with the bench as usual regardless of "owned" champions.
3. Maybe bring bans back for ranked ARAM, bans are important in ranked both for strategy and simply pointing out which champions might need some adjustment to keep from being oppressive.
I think these changes for a ranked mode (with number tweaking) would be enough to make Ranked ARAM viable and competitive without eliminating the randomness that makes it ARAM.
Please let me know if there are any major issues I've overlooked.