Just...no. I love ARAM and even play it more than 5s nowadays. However, it's because the mode is fun. There is definitely a level of skill involved specific to this mode, but most matches are determined before the game starts as long as the general skill level of both sides is somewhat comparable. There's just too much chance involved to be able to compare players in skill at a competitive level. You would likely have to play 50-200+ matches in the ranked mode before knowing roughly where you belong due to all that chance.
Also, if that happened then fewer people would be in the non-competitive ARAM, making makes matchmaking take even longer or be even more lobsided skill-wise.