Posting as someone that mainly plays ARAM's nowadays. I'm usually matched with (https://na.whatismymmr.com/plscheckthisbush) anywhere from Platinum -> Challenger players (got to play against GCU's Rikara on Fizz, was hilarious and fun!: http://imgur.com/a/eCzbq ), and the amount of dodges I encounter on a daily basis is rather confusing, mainly because there's so much freedom to play off-meta builds and have a gold income that would otherwise be very difficult to achieve. But that's the fun of it - facing teams of exclusively Lux/Sona/Morgana/Caitlyn/Nautilus every game sure isn't super fun, and neither is sitting in queue for >20 minutes while the guy that got Urgot dodges 15 times and relogs into his other "perfect ARAM accounts" to dodge again. I'd much rather have 5 melee vs. 5 melee brawling it out in the middle of the map.
I don't own Varus, Lux, Sona, Caitlyn, Zyra, or many other incredibly common ARAM champion simply because they are very boring to see and turn the game into a one-sided match rather quickly. With that being said, however, I find that these champions are nearly always in a game, and tend to boast some of the highest winrates around. I'm always VERY excited to see 2 teams actually fighting and defending one another making the best of what they have. We have 5 AD Champions? Looks like I'm going AP Rammus full Sonic mode into their team. We have 5 AP Champions? Sick, AD Annie looks fun to try.
The ONLY time I ever dodge is if something pressing immediately comes up in real life during champion select (has only happened once over many years of playing) or (as OP has said) playing the same champion several times in a row - and even then it's extremely rare, as I'll likely have a reroll or can trade with someone. I'd imagine I dodge a total of 1-3 times a month at most, usually when I'm burnt out of playing said champion over and over. I don't mind playing Rek'Sai a few times, as she will always be my main and best grill/bae, but after 3-4 games in a row I'd like to try my hand at something a tad more mechanical. I don't want to play Sona 10 games in a row and pubstomp the enemy team into pulp rolling my face across my keyboard and building 6 tears because I can, that's just boring and counterproductive to the game mode. I'd much rather play Tank Janna and spam "AND YOU THOUGHT IT WAS JUST A HARMLESS BREEZE" as I dive into the enemy team. That's much more fun.
In short, I feel that while the ARAM penalties are already much steeper than Summoner's Rift (15 minutes 1st dodge, 30? for the 2nd, no idea after that) I don't think the lack of "you have to be a team player at some point" is enforced. I believe the problem is compounded by ARAM-only accounts playing only the top champions for the mode.
Hopefully, in the future, Riot will implement something of the nature of "keep X champion until you play it" for ARAMs, or unlocking a larger champion pool for the player-base while limiting the ability for players to relog to their umpteenth account for 30 minutes to only play "OP Champions." The only problem I see with this is players who tend to play together in ARAM could create accounts with only ARAM-based champions, and dodge specifically when they have a great champion just to hold onto it and stack their teams in the future with others that do the same. Also, this would be very awkward for 2 people who dodged while both having, say, Urgot. At that point I'm not sure how the priority would go to who gets the free reroll, however I'm sure they could have some sort of matchmaking protection against placing those players together - although that would likely require a moderate-to-large amount of resources devoted to only coding it, and I don't believe ARAM's are as high priority as their main map/mode - Summoner's Rift.