Probably because it evolved very early (like before bilateral symmetry, multi layer body cavity, or kidneys early... maybe even before multicellular animals early) and so has been incorporated as an essential pillar into multiple processes layered on top of that fundamental architecture.
You've merely stated observations about the context and the process that led to it. That doesn't in any way answer the question of what it's actually doing that's so essential.
My point is that, in a higher organism, it may be essential to how a lot of their processes function, in that it was infrastructure that already existed at the time those processes were developed, so they were in turn developed to depend upon it.
So "the reason it originally exists" and "what breaks if you take it away" aren't necessarily the same thing.
As with, say, digestion, or an major organ like the liver, it's reasonable to think that it does simple things in simple animals, and more complex things in more complex ones.
Take out an animal's liver, it's not one process that stops working, it's dozens. There's one or two that will kill it quicker, so those are the ones it dies of, but artificial livers are hard to build as they implement so many vital processes.
I don't dispute any of that but it's stating the obvious, it's nothing more than topical conjecture (even if it's almost certainly correct), and (most importantly) it does nothing to answer the question. What essential functions are being performed?
Take your liver example. We can largely answer that same question. I can't off the top of my head but the answer is fairly well established even if incomplete to varying degrees depending on the species.
There is widespread consensus on why a liver is needed for survival whereas there is not for sleep. That's particularly interesting when you consider that sleep is more common across the tree of life than dedicated livers are (at least AFAIK).
Sleep is more common across the tree of life because it's older.
Older than bilateral symmetry even - jellyfish are thought to sleep, sponges however do not. Jellyfish don't have spinal columns, lungs, gills, livers, kidneys, hearts, guts or blood, but they do have nerves and they do seem to sleep.
There is widespread consensus as to which processes failing will kill you first in acute liver failure, but it governs dozens of processes that, medium term, are essential to life; not all are widely understood.
In the case of sleep, it seems to be nervous system dysregulation that kills. It's notable that comatose patients don't seem to suffer the ill-effects of sleep deprivation. But still, "the thing that kills an animal subject to extreme sleep deprivation" is not necessarily "the original process for which sleep was evolved".
Human brains do some fairly complicated vital things during sleep (REM, spindles, slow wave activity), but that can't be the original essential function - the simplest animals that sleep (jellyfish) don't really have brains, although they do have nervous systems.
Whereas those animals which lack nervous systems (sponges) can't be said to sleep, although it's reasonable to ask.. "how would you tell?", or ask whether the question itself makes sense for something that lacks the ability to sense, plan, act.
So another framing is "anything which can be awake, must also be asleep". But one might equally argue, we don't know why animals are awake.
We can go one step further and suppose that, in order for an animal to act, to exercise will, it must do so at above its average metabolic rate, and in doing so it necessarily incurs metabolic debt.
If he articulated a particular essential process and why it depends on sleep in an incidental manner that might make for a reasonable hypothesis. However it would not refute the earlier (cited) claim that there is no consensus.
As presented without any concrete information about the processes involved it doesn't even qualify as a hypothesis, merely empty handwaving. In context it's even worse, being an entirely baseless contradiction of a claim pulled from a prominent paper.
I never agreed with him but all of that is implied. It being informed speculation included.
Also there being no consensus means most scientists who touch on the topic are FFA speculating except the person stating there is no consensus in the overview. It's not "settled science" but rather the opposite.
The question was "why is it needed". In context the meaning is clearly to ask what it's doing that's essential and (it follows) why those things are essential.
The subsequent response did not (as you suggest) articulate some subset of nonessential things done during sleep. Rather it rattled off plausible (and widely understood) aspects of the process that could have led to the current situation. Even if it had listed concrete activities that would still not have made for a meaningful answer.
The first clue that something is wrong should be that the linked article is recent and prominent. Thus short a brand new groundbreaking development we can be reasonably certain that a random commenter on the internet will not be sensibly rebutting the claims (and certainly not in the span of ~2 sentences).
No that was not the question. Why precisely sleep is essential is a complete non-sequitur to the original question, which was "does something occur during sleep which resembles what is described in TFA such that it can justifiably be called sleep."
As a general rule of thumb, if you find someone's responses incoherent, it's good practice to check what is actually being discussed.
I've always assumed its spontaneous specialization of species: leaving the safety of their nest at those times of day when they are the fittest to occupy a niche.
Once energy conserving "sleep time" exists, the genome can postpone or schedule for activity during these times of day, if it turns out to be more effective somehow.