Some good points were made in a couple of earlier threads regarding snowballs and balance. I'd like to sum them up in a single, hopefully troll-free thread (haha yeah right).
1) There is a serious problem in ARAM w/ the overwhelming advantage that certain pokers (Ziggs, Lux, Xerath, Sona, etc.) have when played well. This is exasperated by people making smurf accounts and only buying pokers or other ARAM-uber champions. It is worth noting that having a good tank can often trump this, as this data (courtesy of http://lolbuilder.net/news/aram-champion-distribution shows):
Champion Win Rate Play Rate
Sona 63.21 1.08 --> POKE, heals, mobility
Heimerdinger 63.17 1.62 --> POKE, stun, turrets
Kog’Maw 62.74 0.55 --> POKE, ad/ap versatility
Ziggs 62.32 0.83 --> DEAR GOD THE POKE, why are people rerolling him??
Galio 61.56 0.28 --> Ult/counterpoke
Lux 60.5 1.34 --> Poke
Sion 59.16 0.67 --> RAWR
Fiddlesticks 58.55 1.32 --> If you don't understand this, you won't understand anything I say.
Maokai 57.86 0.42 --> He pokes, he tanks, he dives, he aoe's... why reroll him?
Vel’Koz 57.83 0.55 --> Poke and ult. If people learned to use his q it'd be higher.
2) There are certainly champions that everyone rerolls in ARAM because of the nature of having a single lane. In other words, while there are good champs, there are also very bad ones. You can find lolbuilder's full list of data at the link below, but in brevity here are the Hall of Shame inductees:
Champs with 45% of lower win rates in ARAM (in order): Eve, Akali, Kha'Zix, LeBlanc (which blows my mind), Rek'Sai, Tristana, Aatrox, Fizz, Elise, Lee Sin
I would note that there is a weak correlation between win and play rates. This means that a lot of people just "don't get" some of the champs that are the best at ARAM, or are so concerned with getting poke they overlook (reroll/dodge) things like - gasp - counterpoke. Note that a win rate above 50.00% means that on average, this champ will win in ARAM. People complain about poke, yet reroll diving tanks and other counter-poke. Everyone wants to be the hero with the big stats instead of team players, and this means that lots of less glamorous champs with WINNING records don't get picked. A few excerpts:
Champ_______________Win Rate______Play Rate___Comment
Sejuani_______________50.42________.25________ADC can't get to squishy poker? Dive/stun/ggez
Galio ________________61.56OMG_____.28______This is the fifth highest win rate in ARAM, but no one plays him.
Master Yi_____________49.83(wow)_____1.84_____Everyone fears/targets, Yi, but on average he loses.
3) OMG get to the point n00b. My point is that there really is a problem - ARAM smurfs, poke balance where the pokier team often wins, and champs that simply aren't balanced around the ARAM concept. Snowballs are a viable fix for that, HOWEVER there are a few changes I'd recommend to stop them from utterly dominating every aspect of ARAM play the way they do currently.
A) Range. I think everyone can agree that Blitzcrank has sufficient range for great openers. Slightly more range that Blitz would be fine, but current range is dominating gameplay.
B) Cooldown. 20 seconds. Seriously?? How about 90? That's still significantly lower than all other summoner spells, but it stops EVERY SINGLE PLAY from revolving around snowballs. Now only half of them will.
C) Synergy. This isn't so much a new reason as a justification for the previous two. Blitz, Yi, Katarina, Galio, Malphite... all of the top picks for LotPK have amazing abilities that rely on setting up the perfect moment to use them. Snowball every 20 seconds takes the skill out of the setup and turns Yi into the faceroll champ people think he is.
4) Snowball fixes ARAM. Poke is no longer the only viable option (though data shows it wasn't before...), and there should be no more GGs at champ selection. But 20 seconds and 999999 range is turning ARAM into LotPK instead of fixing the problem.