The problem with ARAM Soraka is that any team with her instantly has a designated kill order. Take out the ADC(if there is one), then knock out Soraka from the fight. She has no resistance to dives and no real combat capability besides starfall. Plus, taking her out fast ends ALL her potential, unlike with Karthus. Her one real try at self-defense is the liandrys/rylais shred build, and that cuts into the AP of her heals. She provides substantially less utility than MANY of the other supports that can be picked up, and becomes less effective the bigger the teamfight gets, which is a pretty silly weakness to have in ARAM.
Ashe, also, is someone I'd avoid picking up for this account. She does a few different things at a mediocre level, and nothing particularly well. Her base stats are on the low side, and she has no steroids, natural or otherwise. Her greatest weakness is probably her slow mechanics, which bait the player into picking up manamune to sustain constant volley spam. Slows in ARAM are basically useless against any team that had any sort of counterplay at all. The volley damage itself is on the low side unless you hard stack AD instead of attack speed and crit, and manamune also eats into damage output. Altogether, she can be outdone hard by other ADCs in this format.
As for my dream pickups, they would basically be something like the following:
Pure ADC - Ezreal(doubles as AP), Kog'maw(Doubles as AP), Caitlyn, Varus
AP - Nidalee, Sona, Lux, Malzahar(Doubles as AD and you will never convince me otherwise), Morgana, TF(doubles as AD), Viegar(rage-inducing stun).
Tanky initiators - Blitzcrank, Amumu, Galio, Leona, Jarvan, Maokai.
Bruisers and assassins - Kha'zix, Jayce, Diana, Zed
That's pretty much a killer pool to draw from. I'm noticing that most of these champions have at least one of the following: Overpowered poke, very hard engage, or incredible team utility. Any of these champions would be useful in any team composition. If I had four other AD carries on the team, for example, I would still keep Caitlyn if I rolled her.
After that, I'd probably wind up picking up things that I'm pretty good with, for utility purposes, Something like:
Fiddlesticks(E poke, 3 second CC, and phenomenal ult)
Alistar(with an Iceborn Gauntlet, his CC and combat ability becomes absolutely retarded)
Kennen(manaless and AP/AD fluidity)
Gragas(powerful zoning ability)
Thresh(hooks OP)
Nautilus(dem hookers)
Orianna(poke)
Zyra(CC and unexpected damage output)
Akali(her level 6 bullshit)
With 30 owned champions in the pool, that makes it somewhat unlikely that I'll random into something I really need to waste a reroll on. I expect most of the time I'll be rerolling just free-week stuff.