I'm not sure I understand what you are saying here. If "meaningful consequence for failure" is synonymous with "the opposite of success" then it exists for anything you attempt. Which would make it a meaningless term. Which suggests to me that this is not what the authors intended.
In this context, no meaningful consequence of failure is being taken as, "no meaningful difference between success and failure".
I roll to walk across the room. If success means, "I walk across the room" and failure means, "I walk across the room, but slightly less gracefully," then, in most circumstances, there are no meaningngful consequences and it's pointless to roll.
Similarly, a task you will succeed at eventually, when there is no time pressure and you get unlimited retries, has no meaningful difference between success and failure. However if, for some reason, you only get one try, then the opposite of success is meaningful, because you're now stuck dealing with that outcome.
Let's pick a simple scenario: there's a locked door, and no time pressure. The thief has a 60% chance to pick the lock. If he succeeds he opens the door and the party finds a treasure room and gets loot. (Yay!) If he fails, there's no change to the status quo.
Why (other than history/tradition) should this be resolved by a roll, rather than just letting the thief succeed? What does that actually add to the game?
If multiple attempts are allowed and there is no reason to care how long it takes, then I would not roll.
I think the answer might be, "Because it creates a branch in the narrative: if he succeeds the story goes one way, if he fails the story goes the other." That's true, but why it important to leave that to RNG? You have a GM and a bunch of players all contributing to the story, which creates lots of branches.
I mean, to me, using dice to resolve uncertainty is the whole point. Asking, "Why use RNG when there are already lots of branches?" is completely missing the point.* Creating branches is an outcome, but it's not necessarily the point. I'm using RNG to resolve uncertainty because that's fundamental to the game I'm playing -- we do stuff, and when we reach a moment where the outcome matters and is also uncertain, we turn to the dice. I've just been reading Mythic GM Emulator recently, and it's not dissimilar to the Oracle questions there. You can ask "Is the angry ogre in this room?" and the answer may well just be, "No."
We can argue back and forth about what constitutes a situation where it matters, but I'm not terribly interested in locking it down to a particular set of inviolable rules. I've got a pretty good feel for when it matters to me, and that feel seems to work well for our group, which is all I need.
*To be clear, it's missing the point with respect to my game style. I presume that, within the context of your own style, it's entirely the point.