See, that's the point of providing that link from Extra Credits -- if you're providing the Far Realm as just another monster-generator, and that humanity can ultimately understand and even triumph over the Far Realm, then you're doing it wrong. Sure, you can say that it's more fun of a game to be able to beat up Cthulhu (or Zeus, or Odin), and if all you want is a nice, escapist game that doesn't have any bearing or connection on the greater issues of existence, that's fine.
Personally, I'm not into that kind of games (mass invasions, world-ending threat, kill the uber unspeakable evil). I was just pointing that, taking the idea that sparked this discussion (Far Realm aberrations invading Toril through holes in the Wall of the Faithless), if you use the far realm in a game, and have aberrations wreak havoc in a full fledged, Hollywood-style invasion, then going for ''mystery'' and making the players feel powerless (or really limited), kinda makes the premise not really suitable for the atmosphere that game aims to create. As the video that you linked says, evoking such a feel requires to use the Far Realm creatures as obscure, ever creeping presences, not as ''in your face'' invading monsters.
The whole point of Cthulhu or the Far Realm, from a philosophical perspective, is to remind us that humanity is a speck, a smear of chemicals that somehow managed to become self-aware but is constantly standing on the verge of extinction, either at the whims of powers it can never comprehend, or simply by venturing out into a universe that simply doesn't care that it exists and finding that it has no place there.
The first paragraph of "The Call of Cthulhu" by Lovecraft himself puts it best, I think:
"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age."
Our Universe doesn't give a crap that we exist, that's true. As you put it, life is yet another natural process, more complex but not really different from a rock falling. However, we definitely do have a place in this Universe, otherwise we wouldn't exist. The fact that we are a ''smear of chemicals'' doesn't mean that we are meaningless: we function according the laws of the Universe, just like everything else, but --differently from the other ''specks''-- we have managed to understand much, and even use it to our advantage.
I don't agree that humanity has gone beyoned what ''was meant for them''. There isn't anything specific that is meant for us, except existing within the context of the Universe (and we don't even know if that was actually ''meant'', we just know that it happened). That isn't to say that humanity is limitless, but implying that learning how the Universe works is ''not meant'' for us is a baseless claim.
Returning to the Far Realms, we do have the possibility of understanding this Universe, and what exists within it. This is why I pointed out that, the moment the monsters from the Far Realm manage to exist within the Universe, they are subject to its rules, and the people of said Universe could understand how ''they work'', because even chaos or madness are just results of the laws of nature, and follow patterns.
The only reason that the illithids haven't already put out the sun, or the aboleths haven't already flooded the world and made us all their jelly-covered slaves, is that those creatures exist in our stories, and we cast ourselves as the heroes in them. Most of us enjoy those stories, which is fine, but let's not confuse the ability to cast ourselves as the heroes in our own stories with the ability to actually overcome the unknowable and defeat the unthinkable. That way really does lie madness.
--
Pauper
I don't agree with this. We have mutiple concrete examples of ''overcoming the unknowable'' in our history. ''Unknowable'' is a matter of perspective, and a lot of what was considered such in the past, can be now understood, and even simulated or predicted, through math. As I've already said, if something exists in this world, and can interact with us, then it works according to the laws of nature