Well...I see the larger problem as the fact that instead of feeling compassion for a sad/sick friend everyone seems to want them to go away. I'm not trying to be snarky, but could we all think about that for a second? If you wouldn't want to help them feel better or find out what's wrong, why are you friends with them?
Yes, absolutely people should keep the whining to a minimum. However, just as an example, I'm at the tail end of a very hard semester, in which I've been doing quite well. A few days ago, a monkey wrench got thrown into a few of my projects, and it looked like I was going to have to work twice as hard next semester. I posted, ..."says this semester can't be over soon enough." and got a few sympathetic comments from classmates, and a few moral support comments from other friends. Yes, I post other things, and the majority of my posts are happy, but then I'm generally a happy person. If you friended someone without realizing that they were going to turn into an emotional vampire, isn't that kind of on your own head? Just quietly unfriend. To me, blocking seems a sneaky way of keeping up your friend count while not needing to actually give a crud about the people on the list, or needing to let them know that you don't want to hear from them.
I guess what I'm saying is that doing that, as long as the people on your friends list are ones you actually consider friends, is no different than posting in the 'hugs' folder here. And we wouldn't dream of suggesting that the people who do that stop whining...