Why do people watch sadness?

-- some parts might be considered spoilers --

"One Litre of Tears" keeps staying on my mind.
Don't think of this as an evaluation of the series, but more of a complaint: Why did I watch a story that made me cry so much, and left an aching in my heart? Are human beings just emotion-addicts, who actually enjoy any strong feelings as a kind of entertainment? Putting this so bluntly, I'll anticipate that entertainment isn't the only purpose of movies, and might explain why "One Litre of Tears" is without doubt a 10/10 for me.

At the end of the series, I felt quite relieved as I was really drawn into it and couldn't sleep until finishing it. I concluded that I really enjoyed it, from beginning to end. Especially in the sad moments, I was deliberately enjoying the sorrow. For a while, I thought really badly about human beings: "We feel better ourselves, by watching suffering" (Or another less offensive way to put this is: "We learn to appreciate our own well-being")
Although I'm lucky enough to be generally healthy and didn't have to overcome any challenges of significance, I could so much emphasize with the characters. The moment when Aya was conducting the school chorus was the last unconditionally happy moment of her life. She knew it at that time, and it accompanied her for the rest of her life. Thinking back to that moment caused incredible feelings of happiness and pain at the same time that the series could make me experience like nothing else. It's almost too much emotion to cope with!

Retrospectively, I concluded that it might be a story of hope and the will to keep on living - But in the end the series just depicted the sorrow of a human life, that is gradually ripped apart in one of the cruelest ways I could imagine. Throughout the episodes, and afterwards, I tried to figure out what this series is trying to tell me. Even if some might think different about this, it's not merely a praising of the courage of Aya, or the greatness of her friends and family - That wouldn't at all inspire people in such a way. "Look how great these people manage, even though they face such obstacles". No, the movie is deeper than that, and tries to bring across what Aya is telling the world: "Being alive is enough, keep on living!"
But isn't this a really bittersweet insight, people gain through this? It's a kind of happiness that always comes along with an aching in the heart. Why do people feel 'better' after watching the series?
At that time, I was overcome by an immense melancholy: Aren't we, who are healthy, obliged in some way? Don't we have to live our lives to the fullest, in sake for those who want to be happy but can't? You could even say it made me feel guilty for not enjoying life sufficiently.

A second train of thought - although egoistic - is surely the what-if assumption. What if this happened to me? Even if one might be ashamed to admit it, I guess this is what goes through anyone’s mind all along.
And yet, I feel guilty: After all, I'm certain that I am not as strong as Aya. If I was in her condition, I would undoubtedly want to die. I've been wondering if this is also a part of the human greed that Asou has been in despair of. The greed to want more from life, than nature is giving.
So I am wondering "Would it be wrong to choose not to keep on living?"
I suppose there are cases of the disease, in which the patient chose to end their suffering rather than enduring a mere echo of their previous life. This surely wouldn't be turned into a movie, but should it really be condemned? On the other hand, it feels like abandoning anything that Aya was fighting for. I'm to much of a coward to live a life like Aya and I feel really bad about myself for thinking like that.

To justify my perfect rating, I'll just mention that without watching this I'd never have put so much thought and emotion in a topic like this. A story that gets people to think about life, is certainly one that's worth to be told. Independent of realization, cast, script and all that, very few movies can compete on that level. That's why it deserves to stand out with a 10!
I really appreciate if you read all this until here. (And I'm sorry for my English, can't really tell if it's flawed)

tl;dr: Why do you think do people like to watch sadness? And more importantly, what are you taking with you from this story?