The Buddha didn't just teach that birth was suffering. He taught that "the all" was suffering, "the world" was, the five khandas subjected to clinging. It's clear, I think, that "life is not without suffering," except for one well gone, who's just left with physical pain as the occasions arise.
Not all life is the same, so some might have more suckiness than others. But does it all suck at the bottom of it? Wherever there is clinging, there is suffing. So if there is clinging to life, there is suffing.
I think it's said that no existence, no state of being, is truly desireable. Even a happy life might be undesireable. Certainly preferable to an unhappy life (all other things being equal).
By the way, retro, a picture of a monk smiling, while maybe a nice photo, isn't really a serious kind of argument. We could contemplate that those very teeth may one day be in a garbage bin somewhere, who knows, to say nothing of the skin and internal organs.