You can't balance champs around ARAM.
But there are a few things to note that become obvious in ARAM.
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because champs generate gold quicker, you are allowed to get builds online much faster.
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because of this you can see which champs become stronger/weaker as the game progresses.
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feeding is only temporary when it comes to whose behind. - Unless you're unlucky and have 0 poke or sustain.
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some champions just feel inherently broken and anti-fun to play against. (Trundle and his immense healing/tankiness that can out trade teams with no ADC. Brand popping your tanks to 0 because of his passive. Etc).
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which champions have really poor team fighting capabilities (ARAM is 100% team fighting).
There's a lot of good things about ARAM than can teach you when a champion is a good pick. But I honestly feel like if you get a champ in ARAM that is just too good at everything (Trundle comes to mind; healing, tank, stat stealing + more healing. The passive is really anti fun in ARAM tbh) they should probably be reworked or nerfed.
ARAM shows which champions need reworks more than nerfs, IMO. But because of the nature of the mode, I doubt anyone considers it a good way to balance champs in general. Everything is based on SR, but ARAM allows a quicker glimpse into what a champion can or cannot be.
tl;dr rework Trundle. Thanks.