You're mistaking the purpose of ARAM if "unfamiliar champions" is a concern. One of the big benefits of ranked ARAM is that it (ostensibly, due to the current owned+free champ thing) would reward generalists. All the other existing ranked options favor specialists (e.g. "I'm a jungle main;" I'm a top main;" I'm a Riven main."). In contrast to "how well you play your best champ(s)," ranked ARAM would test "how well you play on average."
Furthermore, if someone receives an unfamiliar champion and thus isn't at optimal performance, that's on them. It's no different from the current ranked options. It's recommended to know how to draft, how to CS, how to ward, how to rotate, and so on, but those aren't strict requirements before playing ranked. There must always be a Lich King Bronze-tier.
I will agree that dodging is a concern, but it's not like any of the other ranked queues have solved that problem either. "Dodge questionable teammates" has long been relatively common advice. Perhaps have dodge penalties accrue over a week/month instead of immediately resetting on completed game to further dissuade dodging?
On a related note, maybe rerolls shouldn't even be allowed in ranked ARAM, to further emphasize the random nature of the mode. Maybe bans should be enabled instead, for the metagaming strategic question of whether you ban overall power picks or ban champs you're personally bad at playing. Maybe ranked ARAM does away with promo series to minimize the impact of RNG. Maybe implement a whitelist/blacklist feature into unranked ARAM, so it's easier to practice a small subset of champs.
tl;dr: There's a bunch of potential changes to consider and discuss, but the basic concept of ranked ARAM is solid.