Other way around. Ranked Draft HA would be a bad idea, but Ranked ARAM would be great, or at least understandable.
Draft HA suffers heavily from stagnation. There simply aren't enough (any?) significant balance changes to shake up the meta. It'd be a similar situation as 1v1, where, aside from minor variations, the same champs would be pick/ban for months, if not years.
Although ARAM has the same balance issues, the randomness mitigates the stagnation. Certain champs are definitely more common, but they're not guaranteed. Furthermore, the fact that the ranked ladder encourages a (large) number of games balances out the randomness. Someone might be lucky for a game or two, but probably not for 50 or 100 games. Lastly, ARAM distinguishes itself from the existing ranked queues by testing players' skills at a variety of champs. Due to the randomness, having a wide champ pool is rewarded, as opposed to the existing ranked options mostly rewarding specialization (e.g. main a position, one-trick a champ).