I've started to notice that a lot of what I hate about the Murder Bridge has nothing to do with the map design or anything of that sort, but rather in the glorious imbalance that almost always happens with regards to team composition. Rarely do I find myself having "fun" as most games boil down to one side being completely outmatched solely because: 1. they have 4 melee champions and are facing 3 long range mages and 2. people were noble enough not to dodge regardless of the horrendous composition.

Would it be possible to change the "all random" feature slightly so that, while players are given random champions, that general roles that fill a team composition are selected regardless? That is to say, while each player will receive a random champion from those they own, each team will at least always have: a tank, a mage, a bruiser, a support, and a carry or some derivative of the aforementioned.

If you can't stand the random, don't play the game. Don't ask for changes that would ruin the fun for those who embrace the game mode for what it is. Just play a draft pick game on PG if you're worried about team balance.

The problem is that there isn't really a set team comp in the sense that there is on SR (and it's not even set in stone on SR). Trying to force the standard SR comp on people in ARAM would just be silly. The point of ARAM is to adapt to the situation you're given and make the best of it. Don't have a tank? Have the whole team build a little extra HP, or choose somebody on the team to play as a non-conventional tank. Team full of mages? Try having one go AD, or else have everybody build void staff so they can't just stack MR against you as effectively.

Messing with the random like this would kill off the entire point of ARAM.

one game we had an AP sona and an AD/CDR lux...because it made sense

aram is meant to throw at you a comp and forces you to make the best out of it.