In regard to the Proving Grounds and ARAM:
1) It was a great idea and helps the ARAM community for the LoL playerbase. It is especially nice that now you don't have to play Summoner's Rift for that type of game with basic rules - no snowball items, no guardian angel, no leaving mid lane, etc.
2) I admit is a fun time to play ARAM and there have been some incredible matches that last 40+ minutes for me going back and forth.
3) It is a nice place with no to little pressure where you can try out new/unconventional things on champions based on the gameplay.
1) Sometimes skill levels are entirely unbalanced in terms of wins and normal/ranked ELO. This regularly leads to very lopsided matches.
2) The lack of a matchmaking system seems like an issue, but I understand that it could be difficult to implement.
3) I know there is the whole point of random, but sometimes the complete random makes the game just incredibly lopsided.
4) People can easily win games by having a team together for a match and win due to more streamlined communication from voice communication software.
1) Implement somehow a matchmaking for the game mode, yet I know it would be difficult.
2) Take away the complete randomness to some degree to make matches somewhat more fun to play without totally being lopsided.
a) One option would be to set up the matchmaking to select any champion even if not owned so that true randomness could occur.
b) Set up the matchmaking to choose somewhat of a balanced team instead of all melee or all tanks - AD, AP, Support, Melee DPS, Tank
c) The above list is obviously the current Meta Game for normal games, but perhaps looking into that would help even out matches. The random generator might not have to exactly fill out that, but mixing the classification of the characters would reduce lopsidedness.
3) I know since it is a custom game mode, there is probably no incentive to make a penalty for people who dodge, but it can decrease the fun when someone constantly dodges and rejoins because he or she is not satisfied with his or her champion.
4) Perhaps for to curve dodging, you might be able to set up character selection to choose 3 random champions of different classification that might fit what the player is looking to play instead of only one champion initially. I know it is a different game, but I do know DoTA (heaven forbid I mention that game here) has something like that in one of its game modes.