So for players who haven't bought champions, ARAM is just no longer a terribly viable mode if they don't want to play, say, Udyr or Mordekaiser?
The problem is that this solution hurts players who are interested in ARAM and don't like certain champions they haven't bought.
Unlock all champions, and we players who are content to play the game in quiet will be listening to every player bitch about how they don't own Shyvana or Nocturne, but have to play them now.
I really don't see this problem as often as everyone suggests it is one, though if I did, I'm not sure this would be my solution either. It's too extreme and disregards what is arguably a large portion of ARAM's playerbase.
A more suitable solution would be to pick a handful of champions who are 'ARAM frees' between hot picks and cold picks, so that free week + the ARAM frees gives some balance. Assuming you have about 30 champions who are 'core hot picks,' if you will, substantiating that between 10 (free week) and an additional 7-10 (for ARAM frees) would probably do just as well while being a healthy compromise.
Why the need for the large-scale, sweeping solution? Doesn't it dawn on anyone that this will also harm players who are just trying to play some ARAM for what it is, with their meager selections of champs?