See, again, you are going for intangibles here that really don't matter- mostly irrelevant really. The Light and Dark sides are part of the Force, sure, but the only way that is ever relevant for us, in any way at all, is in ho that relates to their representation by people. And in that respect, all we ever see- absolute 100% not contradicted- is that the Light Side is good and the Dark Side is evil, and those who have the most power with the Dark Side-which in the original films are the Sith- must be destroyed. Yes, it may well continue to be embodied in people. And this will continue to be a very bad idea and such people must always be stopped.
The balanced galaxy we are shown is one with the Light Side completely triumphant and the Dark Side completely defeated. This is the 'balance' between good and evil. Evil exists, evil goes on existing, but it is good that we must be overwhelmingly favouring; it is evil that destroys balance.
To show one of my points- you say:
"It doesn't disappear if the Sith cease to exist."
To which my answer is- so what? Who cares, if its not being embodied in any way which has power? It's literally irrelevant at that point. Like I said, the existence of the Dark Side in this form is vague; it is taking things to a philosophical level that is so far detached from any worthwhile analysis of film events as to be not worth it.
I'm not really sure what your last comment is getting at at all. I said 'current embodiment' which clearly implies more than one over time, which TFA stated directly. And I will remind you that GL directly and unequivocally stated that balance is restored by getting rid of evil in the universe. Sure, we don't have to overdo it in taking that literally- he doesn't mean the entire concept is annihilated from the cosmos- but it does reinforce the basic point here. He talks of 'dark forces' that destroy the balance of the cosmos- there has never, ever been anything approaching a 'light force' that could do the same, because all the light ever does is aim to restore the balance. What there has never been in the SW story, at any point, ever, is any suggestion or demonstration that the Light Side could ever be a problem in this cosmic equation.
The Light Side is represented by the good guys. They are the ones who do things right. And to remind again: there can be no balance without the Jedi- the champions of the Light Side. They are the ones bringing balance. With their opposite number, the Sith, it's the other way around- the Sith must be destroyed for there to be Balance. So if the champions of the Light Side must exist for balance, and the champions of the Dark must be destroyed for balance, what does that tell you? The connection between the Light Side and balance is so staggeringly obvious that, as I say, it is being wilfully obtuse to deny this. If all we ever see is the Light Side trying to keep the balance and the Dark Side trying to destroy it, then what possible tangible or useful definition or viewpoint can there possibly be other than to say that Balance is represented by the Light side? That is the entirety of the presentation. All that stuff about evil/dark side still literally existing in the balanced cosmos- well, sure. But for any practical purpose- irrelevant. The 'natural balance between good and evil' appears to be one where evil is defeated and good has all the power. Well- that's exactly what it should be. It's only a mistake to see balance as some sort of equal sharing between the two. As we see that evil keeps messing the balance up, that is clearly not the case. Allowing evil such power would leave no hope for balance.
So- the Light Side is represented by good guys. The Dark Side is represented by bad guys. The good guys defeat the bad guys- balance is achieved. Evil might not be literally destroyed but it is defeated, and that is highly significant. And that evil always - always- comes from the Dark Side... because the two are synonymous. Balance is when that evil has no power. Allowing it any power- every time we see it- brings imbalance. That balance is represented by the Light Side.
That's Star Wars- good guys and bad guys Light Side and Dark. Good/Light must defeat bad/Dark. The successful outcome of that- is balance. Complicating it beyond that is to lose your way.