(Written very fast! I have little time, but the argument is...tempting!)
Reading Buddhism with the lens of Schopenhauer "all but Nibbana is suffering" is not a good reading. I would not slightly re-read all the Dhamma also with sister Vajira's eyes (which has a Milindapanna understanding of the aggregates) or with some other sparute passage that can be interpreted in various ways, have no parallel or, in one case, the parallel makes a lot more sense.
The problem is that the
equivalence "all is suffering" (or "life is suffering") fails immediately. In fact not all life is suffering, and it is not certainly so for most of us. Life is a mix of Dukkha and Sukha and neutral sensations that greatly varies between lifes. The human realm is precisely the one in which the Dukkha is there, but not so much to bewilder and incapacitate the being. Even in the four noble truths we see that Birth is Dukkha, Old-age is Dukkha: what about youth without illness? If all is Dukkha, there's no point to distinguish between youth and old-age, or distinguish between separation from the loved or separation from the unloved.
We have to distinguish between feelings of Dukkha, grief, despair, lament, physical pain and the idea of Dukkha, which must be used skillfully and as a raft. The idea "all is Dukkha" is not Dukkha, but an evaluation, a thought, which have its role to make sense of the world, but it is not the actual feeling of Dukkha.
Only when this distinction is understood, I think, there can be meaningful discussion. Life is not only feelings of Dukkha or only-grief: this is, I think, pacific (and I would also say that this "all conditioned is Dukkha" is a bad thing to entertain without the understanding that it is a strategy to arrive at the happiness of non-delight and non-being, because one can miss the dependent-from-craving nature of Dukkha here and now about all the mental dukkha avoiding the happiness of the path: if all is Dukkha, what is the point of removing it? But that would be a digression here).
The only way in which one could say that all experience is Dukkha is that because it is Dukkha because compared to Nibbana everything is inferior and
it is to be abandoned for your own welfare, which can be verified by ourselves and it is well-supported in the canon. But that is a very different message and again a perception/thought to be developed, not the actual feeling of Dukkha per se, it is just the perception of things being "Alien" that should be developed for purpose of dispassion. For example the cauterization of the lepers is Dukkha for the Buddha: why? precisely because he delights with what is
superior: non-delight. But
the feeling for the lepers is not Dukkha and, using the approach of the philosopher:
the impermanent is as good as it gets and as real as it gets and is good enough.
But that totally misses the fact that extirpation (understanding: the dispassion is natural and derives from a knowledge) of desire is happines, that the Arahant is Happy, the Arahant enjoys total-freedom, the path is for your welfare and happiness both now and in the future, and the main question of the Dhamma is "what will lead me to long-term welfare and happiness"?
So let's read the main argument:
For Buddhism, all is dukkha, suffering. All is unsatisfactory. This, the First Noble Truth, runs contrary to ordinary modes of thinking: doesn't life routinely offer us, besides pain and misery and disappointment, intense pleasures and deep satisfactions? How then can it be true that all is unsatisfactory? For the Buddhist, however, what is ordinarily taken by the unenlightened worldling to be sukha (pleasure) is at bottom dukkha. Why?
Because no pleasure, mental or physical, gives permanent and plenary satisfaction. Each satisfaction leaves us in the lurch, wanting more. A desire satisfied is a desire entrenched. Masturbate once, and you will do it a thousand times, with the need for repetition testifying to the unsatisfactoriness of the initial satisfaction. If it were fully satisfactory the first time, why would you be inclined to repeat the pleasure? Each pleasure promises more that it can possibly deliver, and so refers you to the next and the next and the next, none of them finally satisfactory. It's a sort of Hegelian schlechte Unendlichkeit, bad infinity. Desire satisfied becomes craving, and craving is an instance of dukkha. One becomes attached to the paltry and impermanent and one suffers when it cannot be had. One also suffers when the satisfaction sought is achieved but revealed to be less than what one expected.
There is more to it than this, but this is the essence of it. The thing to note is that the claim in the First Noble Truth is not the triviality that there is a lot of suffering in this life, but that life itself, as insatiable desiring and craving for what is unattainable to it, is ill, pain-inducing, profoundly unsatisfactory, and something to be escaped from if possible. It is a radical diagnosis of the human predicament, and the proposed cure is equally radical: extirpation of desire. The problem for the Buddhist is not that some of our desires are misdirected and inordinate; the problem is desire itself. The solution, then, is not rightly-ordered desire, as in Christianity, but the eradication of desire. The root (radix) of suffering is desire and that root must be uprooted (e-radi-cated). It is thus a radical solution.
The unsatisfactoriness of things is due to delight and craving. Dukkha as a feeling is not inherent in experience because it should need to be there all the time, while
Dukkha as an idea of unsatisfactoriness is a problem only for those that search lasting satisfaction in the first place. So for those that craves. This again entails that Dukkha have a reason that can be removed: craving. Even the unsatisfactoriness of life is so because of craving it to be otherwise: you want a different existence (or experience) or non-existence (or non-experience). There cannot be unsatisfaction without the craving to be satisfied or things to be different in the first place.
Same with impermanence: if impermanence is simply that things ends, let's take a trivial example of a good film to make it simple, then it is the desire of the delight not-to finish the Dukkha of the film. That again, is something that is only for one that wants more. And that is why without craving, there's no suffering. Of course, one will not be interest to see the film since delight is no more for what is inferior.
But if, as Buddhism also maintains, all is impermanent, then one wonders whence the standard of permanence derives its validity. If all is impermanent, and nothing has self-nature, then the standard is illusory. If so, then we have no good reason to reject or devalue all ordinary satisfactions. Failure to measure up to a nonexistent standard is no argument in devaluation of anything.
Non-craving is permanent for the Arahant. I will also point out that DELIGHT is the root of suffering, not desire, which is the action of ignorance. It is the fact that inconstant and unreliable things gave us delight that makes us crave and then, in turn, will make us suffer or make us papable prey of suffering. But there's what is reliable that can give us delight too:
and that is the absence of craving and ignorance: "Happiness in whatever ways is found". So the Buddha had
very good reason to devalue all ordinary satisfactions: because
he actually found a superior one with the characteristics that miss from the inferior ones: stability, non-disturbance, constancy, always-available, with no external conditions needed.
Then the question is not if life is Dukkha or not, but "what causes Dukkha in experience". From that point of view one can discover that the maximum pleasure is non-delight, non-being in debt and make renunciation our object of pleasure. This is something that everyone can do by himself, and
his knowledge will be indipendent.
You cannot argue with a monk that have the pleasure of renunciation or even stopped craving and convince him that having a Ferrari would be better. If he can stay 3 weeks with perfect happiness like the Buddha, no King can have the same all the time. At the same for the cessation of identity,
we cannot convince an Arahant that having an identity is better (or even a stream-entrant, that already have this understanding, but he still maintain it):
that doesn't require any argument, it is a self-evaluation indipendent of others that require only little imagination about the future since whatever arises passes away as well.