In LoL, All Random means one team is equivalent to 80% Blind Pick; the other collects a loss.
This has been my experience with Random modes in this game. It doesn't prevent the insanely broken Champions in the respective modes from making it into the match on a constant basis, it just prevents the other team from mounting some sort of response to it. To make matters worse, in All Random modes, there can't be mirrors, so one team is going to end up on top right off the bat thanks to all the roll hedging that occurs by virtue of alt-accounts, rerolls, and Champion trading. At the end of the day, the only thing Random about ARAM or URF most of the time is the 50/50 bet you're taking on which team is loaded with more S-tier Champions.
If we turned all of the current All Random Select modes into Blind Pick, it will achieve a number of things:
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In ARAM, there can be a Ziggs/etc. on both teams. Which means, the WORST situation you could possibly get into is a skill mirror, which isn't all that bad, and certainly beats the situation where one team has a Ziggs and one does not. There would be gameplay with this change.
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You can anticipate with high certainty what people will play, and you have the option of choosing something to counter them. The match isn't lost at the loading screen.
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This isn't a concrete point because it'd be hard to prove, but wouldn't you imagine that the Champion pool that you see would actually be larger than it currently is in League of ARAM Accounts?
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This is a big personal factor for me, but this would enable me to actually lose with a Champion I enjoy playing, which would make the experience much more enjoyable.
Disclaimer: I know the ideal situation is an open roster. But Riot through their inaction on this issue has made it clear to the community that they do not see any issue with Random Select as it is currently implemented despite it not fulfilling its implied intent. This is the reason why I'm suggesting to just open these modes up to Blind Pick. We already see the exact same set of Champions every game in ARAM. All this change would enable is the option to respond to and potential counter the top picks, and eliminate the literal advantage obtained by utilizing alt-accounts. I can't conceive of any negative outcome from this that would overshadow the positive.