For me, it's the gambling part of the risk/reward that need to be handled. I mean, your two first examples are not RNG dependant. A player's mistake is not RNG, nor is bad decision.
After that, for the turnip pull or the judge, there is no way to handle this. A peach player pull out a bob-omb, so what ? We're not going to restart the match or anything. The same goes with a 9 judge. The rule "If Jigglypuff Rest you, stay on the platform (so you don't waste your invicibility) until she wakes up" is not hard to apply, it just fair. Is tripping in Brawl a competitive thing ? Does it help distinguish the good from the very good ? Back in the days, if there was a tripping switch in the game, you can be sure that it would turned off day one. But, there wasn't, and there is no rule that counter that mechanic (like "Don't punish a tripping opponent" ? impossible, there is so many case to handle, like if you was charging a smash or whatever). Anyways, here i'm not talking about removing all randomness, I'm talking about reducing it.
Imo, Rest is a super high risk / high reward move, because of the super high endlag and the small hitbox. You actually landed it at killing percentage, and your opponent is dead ? Good... Oh, nevermind, he was insta-KO, now your gonna eat that fully charged Fsmash. Too bad... Now look a the judge, it's like a normal attack, it come up decently fast, can be executed mid air or grounded, has "normal" range/end lag/damage output. But his high risk / high reward comes from the number, and there is not need to change that. The judge only pulling out the 6 like in HRC would be bad for fight plays, resulting in a just "ok" attack.
Finally, it juste about making move balanced by influcing the game by applying rules. I'm pretty convinced that many people prefer refer to the game mechanics, and i'm fine with it, it's already the case.